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Evolution and Evaluation of the Penalty Method for Alternative Graphs Moritz Kobitzsch, Marcel Radermacher, and Dennis Schieferdecker {kobitzsch,schieferdecker}@kit.edu, marcel.radermacher@student.kit.edu Institute of Theoretical Informatics -

  1. Related Work what has been done before? (2) "Alternative Route Graphs in Road Networks" [B ADER ET AL . 11] penalty method (classical method) → putting penalties on arc costs → based on Dijkstra (sec.) no alternative route extraction quality measures numeric values hard to gauge do not directly translate to quality of alternative routes 4 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  2. Related Work what has been done before? (2) "Alternative Route Graphs in Road Networks" [B ADER ET AL . 11] penalty method (classical method) → putting penalties on arc costs → based on Dijkstra (sec.) no alternative route extraction quality measures numeric values hard to gauge do not directly translate to quality of alternative routes 4 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  3. Related Work what has been done before? (2) "Alternative Route Graphs in Road Networks" [B ADER ET AL . 11] penalty method (classical method) → putting penalties on arc costs → based on Dijkstra (sec.) no alternative route extraction quality measures numeric values hard to gauge do not directly translate to quality of alternative routes 4 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  4. Related Work what has been done before? (2) "Alternative Route Graphs in Road Networks" [B ADER ET AL . 11] penalty method (classical method) → putting penalties on arc costs → based on Dijkstra (sec.) no alternative route extraction c ( a ) � quality measures := totalDist D H ( s, u ) + c ( a ) + D H ( v, t ) a =( u,v ) ∈ A H numeric values hard to gauge � a ∈ A H c ( a ) averageDist := D ( s, t ) · totalDist do not directly translate to quality of alternative routes maximize totalDist − ( averageDist − 1) s.t.: averageDist ≤ 1 . 1 decisionArcs ≤ 10 4 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  5. Optimization Potential what can we do better? current state-of-the-art fast "one-hop" alternative routes slow alternative graphs goal fast alternatives with diverse structure approach focus on penalty method ⇒ improve for interactive use (speed-up techniques) ⇒ extract alternative routes (quality criteria similar to via-node approach) ⇒ analyze quality & structure of results 5 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  6. Penalty Method generic workflow 1 while { termination condition false} do 2 {compute shortest path} 3 4 {add penalties to graph} 5 6 7 end 8 9 {select shortest paths + combine to alternative graph} 10 11 {extract alternative routes} path selection fast computation penalization (not covered today) alternative route extraction (modified from previous work) (not in previous work) 6 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  7. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  8. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  9. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  10. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  11. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  12. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  13. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  14. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  15. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  16. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  17. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  18. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  19. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  20. Penalty Method path selection basic approach (classical method) perform "enough" iterations ⇒ generate set of shortest paths select good subset for AG (implementation details left open) when query times matter... (our approach) exploit quality measures ⇒ terminate as paths become too long (allow maximum stretch w.r.t. original metric) ⇒ select path for AG after each iteration (w.r.t. stretch, sharing measures) 7 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  21. Penalty Method computing shortest paths (1) challenges compute many shortest paths ⇒ Dijkstra’s algorithm [D IJKSTRA 59] → used by previous work (takes seconds on random queries) ⇒ static speed-up techniques (AF , CH, HL, . . . → costly preprocessing) arc costs change ⇒ Customizable Route Planning (CRP) [D ELLING ET AL . 13] → used by our approach (takes milliseconds on random queries) 8 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  22. Penalty Method computing shortest paths (1) challenges compute many shortest paths ⇒ Dijkstra’s algorithm [D IJKSTRA 59] → used by previous work (takes seconds on random queries) ⇒ static speed-up techniques (AF , CH, HL, . . . → costly preprocessing) arc costs change ⇒ Customizable Route Planning (CRP) [D ELLING ET AL . 13] → used by our approach (takes milliseconds on random queries) ⇒ but still requires some kind of preprocessing 8 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  23. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  24. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  25. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  26. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  27. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  28. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  29. [D ELLING ET AL . 13] 1 Penalty Method [D ELLING &W ERNECK 13] 2 computing shortest paths (2) CRP preprocessing structural preprocessing takes minutes to hours (required once, can be done offline) multi-level partitioning adding shortcut arcs (boundary nodes of each cell become cliques) metric customization compute shortcut costs (required when arc costs change) takes seconds 1 / tenths of a second 2 (using multiple cores and vector units) 9 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  30. Penalty Method computing shortest paths (3) adaptive customization only update cells with changes only update k levels ⇒ restrict query algorithm to k levels ⇒ preprocessing times ⇐ ⇒ query times ⇒ beneficial for short queries (less overhead) dynamic level selection (depending on hop count, optimized on different query set) 10 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  31. Penalty Method computing shortest paths (3) adaptive customization only update cells with changes only update k levels ⇒ restrict query algorithm to k levels ⇒ preprocessing times ⇐ ⇒ query times ⇒ beneficial for short queries (less overhead) dynamic level selection (depending on hop count, optimized on different query set) 10 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  32. Penalty Method computing shortest paths (3) adaptive customization only update cells with changes only update k levels ⇒ restrict query algorithm to k levels ⇒ preprocessing times ⇐ ⇒ query times ⇒ beneficial for short queries (less overhead) dynamic level selection (depending on hop count, optimized on different query set) 10 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  33. Penalty Method computing shortest paths (3) adaptive customization only update cells with changes only update k levels ⇒ restrict query algorithm to k levels ⇒ preprocessing times ⇐ ⇒ query times ⇒ beneficial for short queries (less overhead) dynamic level selection (depending on hop count, optimized on different query set) 10 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  34. Penalty Method computing shortest paths (3) adaptive customization only update cells with changes only update k levels ⇒ restrict query algorithm to k levels ⇒ preprocessing times ⇐ ⇒ query times ⇒ beneficial for short queries (less overhead) dynamic level selection (depending on hop count, optimized on different query set) ⇒ tens of milliseconds for query and customization 10 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  35. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  36. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  37. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  38. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  39. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  40. Penalty Method alternative route extraction (1) how to extract alternative routes? take constituting routes? ⇒ misses synergy effects take any route? ⇒ arbitrarily bad our approach: CRP- π two-step procedure (via-node & penalty methods) extraction on small graph (expensive methods become feasible) 11 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  41. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  42. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  43. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  44. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  45. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  46. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  47. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  48. Penalty Method alternative route extraction (2) procedure 1. via-node approach based on X-BDV → local optimality disabled (not applicable in AG) exhaustively compute routes keep all routes 2. penalty method based on classical penalty method → initialize with X-BDV routes fixed number of iterations (stretch no good termination criterion) keep good routes (w.r.t. quality measures) 12 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  49. Experimental Setup hardware/software 4 Intel Xeon E5-4640 @ 2.4 GHz, 512 GiB RAM (32 cores, total) Ubuntu 12.04, gcc 4.6.1 (full optimizations) data road network of Western Europe (provided by PTV AG) directed, weighted graph, single SCC 18 million vertices, 24 million arcs (degree two vertices removed) travel-time metric 1 000 queries at random / data point (of random Dijkstra rank / of fixed Dijkstra rank) 13 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  50. Runtime Analysis iterations of penalty method 20 classical our approach 15 Iterations [#] 10 5 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 14 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  51. Runtime Analysis engineering impact classical 10000 Query Time [ms] 1000 100 10 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  52. Runtime Analysis engineering impact ● classical ● +new selection & penalties ● 10000 ● ● ● Query Time [ms] 1000 ● ● ● 100 ● ● ● ● 10 ● ● 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  53. Runtime Analysis engineering impact ● classical ● +new selection & penalties ● 10000 ● +crp ● ● ● ● ● ● Query Time [ms] 1000 ● ● ● ● ● ● ● 100 ● ● ● ● ● ● ● 10 ● ● ● ● ● ● 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  54. Runtime Analysis engineering impact ● classical ● +new selection & penalties ● 10000 ● +crp ● ● +both ● ● ● ● ● Query Time [ms] ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 ● ● ● ● ● ● ● 10 ● ● ● ● ● ● 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  55. Runtime Analysis engineering impact ● classical +new selection & penalties ● ● 10000 ● +crp ● ● +both ● +both +adaptive customization = CRP− π ● ● ● ● Query Time [ms] ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● ● ● ● ● 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  56. Runtime Analysis engineering impact – multi-cores ● cores 1 2 4 8 12 16 ● ● 10000 ● ● ● ● ● ● ● ● Query Time [ms] ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 100 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● ● ● ● ● 1 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 Dijkstra Rank 15 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  57. Quality Analysis alternative graph quality algorithm rating queries decision arcs 3.21 100 ≤ 10.0 [B ADER ET AL . 11] 2.89 1 000 7.0 [R ADERMACHER 12] CRP- π 3.32 1 000 (unfiltered) 17.4 CRP- π 2.89 1 000 (filtered) 9.5 comparable results to previous penalty methods best previous work only considered tiny test set filtering to reduce decision arcs ( ≈ 100 µ s) only for comparison to previous penalty methods reduces potential for extracting multiple alternative routes (not applied in subsequent alternative route analysis) 16 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  58. Quality Analysis alternative route quality # algorithm success [%] stretch [%] sharing [%] optimality [%] 1st X-BDV 96.0 10.0 41.8 75.4 X-CHV 89.6 80.4 40.6 68.1 CRP- π 96.3 42.9 31.9 26.9 2nd X-BDV 87.6 13.8 59.5 65.1 X-CHV 72.5 269.0 57.6 57.2 CRP- π 84.0 47.6 45.9 22.1 3rd X-BDV 75.5 17.2 65.6 54.6 X-CHV 51.4 214.0 63.6 46.8 CRP- π 62.9 67.4 51.8 15.9 comparable success rates (corresponds to runtimes) reasonable path quality measures (lower stretch ⇐ ⇒ higher sharing) limited similarity to via-node alternativs (77.9% | 72.7% | 65.5%) 17 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  59. Quality Analysis alternative route quality # algorithm success [%] stretch [%] sharing [%] optimality [%] 1st X-BDV 96.0 10.0 41.8 75.4 X-CHV 89.6 80.4 40.6 68.1 CRP- π 96.3 42.9 31.9 26.9 2nd X-BDV 87.6 13.8 59.5 65.1 X-CHV 72.5 269.0 57.6 57.2 CRP- π 84.0 47.6 45.9 22.1 3rd X-BDV 75.5 17.2 65.6 54.6 X-CHV 51.4 214.0 63.6 46.8 CRP- π 62.9 67.4 51.8 15.9 comparable success rates (corresponds to runtimes) reasonable path quality measures (lower stretch ⇐ ⇒ higher sharing) limited similarity to via-node alternativs (77.9% | 72.7% | 65.5%) 17 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  60. Quality Analysis alternative route quality # algorithm success [%] stretch [%] sharing [%] optimality [%] 1st X-BDV 96.0 10.0 41.8 75.4 X-CHV 89.6 80.4 40.6 68.1 CRP- π 96.3 42.9 31.9 26.9 2nd X-BDV 87.6 13.8 59.5 65.1 X-CHV 72.5 269.0 57.6 57.2 CRP- π 84.0 47.6 45.9 22.1 3rd X-BDV 75.5 17.2 65.6 54.6 X-CHV 51.4 214.0 63.6 46.8 CRP- π 62.9 67.4 51.8 15.9 comparable success rates (corresponds to runtimes) reasonable path quality measures (lower stretch ⇐ ⇒ higher sharing) limited similarity to via-node alternativs (77.9% | 72.7% | 65.5%) 17 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  61. Quality Analysis alternative route quality # algorithm success [%] stretch [%] sharing [%] optimality [%] 1st X-BDV 96.0 10.0 41.8 75.4 X-CHV 89.6 80.4 40.6 68.1 CRP- π 96.3 42.9 31.9 26.9 2nd X-BDV 87.6 13.8 59.5 65.1 X-CHV 72.5 269.0 57.6 57.2 CRP- π 84.0 47.6 45.9 22.1 3rd X-BDV 75.5 17.2 65.6 54.6 X-CHV 51.4 214.0 63.6 46.8 CRP- π 62.9 67.4 51.8 15.9 comparable success rates (corresponds to runtimes) reasonable path quality measures (lower stretch ⇐ ⇒ higher sharing) limited similarity to via-node alternativs (77.9% | 72.7% | 65.5%) 17 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  62. Conclusion Summary first fast implemenation of penalty method, suited for interactive use (utilizing vector units and multi-core capabilities of modern CPUs) extracted routes of high quality, and distinct from via-node approach (first quantitative analysis of extracted routes from alternative graphs) Open Problems general classification scheme for good alternatives (set of criteria, not tailored to a specific approach) improve runtime to compete with via-node approach (combination with [P ARASKEVOPOULOS &Z AROLIAGIS 13] seems promising) 18 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  63. Thank you for your attention! Time for questions! 19 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  64. References [D IJKSTRA 59] A Note on Two Problems in Connexion with Graphs [A BRAHAM ET AL . 10] Alternative Routes in Road Networks [B ADER ET AL . 11] Alternative Route Graphs in Road Networks [D ELLING ET AL . 13] Customizable Route Planning [D ELLING &W ERNECK 13] Faster Customization of Road Networks [P ARASKEVOPOULOS &Z AROLIAGIS 13] Improved Alternative Route Planning [R ADERMACHER 12] Schnelle Berechnung von Alternativgraphen 20 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  65. Appendix backup slides 21 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  66. Motivation why consider alternative routes? business perspective provide options (users have varied preferences) overcome flaws in model and data (shortest paths need not be best in reality) research perspective building blocks (traffic simulation, stochastic routing) hard optimization problems (quality guarantees) 22 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  67. Motivation why consider alternative routes? business perspective provide options (users have varied preferences) overcome flaws in model and data (shortest paths need not be best in reality) research perspective building blocks (traffic simulation, stochastic routing) hard optimization problems (quality guarantees) 22 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  68. Motivation why consider alternative routes? business perspective provide options (users have varied preferences) overcome flaws in model and data (shortest paths need not be best in reality) research perspective building blocks (traffic simulation, stochastic routing) hard optimization problems (quality guarantees) 22 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  69. Motivation why consider alternative routes? business perspective provide options (users have varied preferences) overcome flaws in model and data (shortest paths need not be best in reality) research perspective building blocks (traffic simulation, stochastic routing) hard optimization problems (quality guarantees) 22 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  70. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  71. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  72. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  73. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  74. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  75. Related Work peering into the distant past... simple approaches to find distinct routes k -shortest path (meaningful alternatives only for large k ) multi-criteria optimization (distance ⇐ ⇒ difference) time-dependent routes (alternatives not guaranteed, limited data) insufficient solutions to the problem 23 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  76. Penalty Method penalization (1) requirements enable discovery of diverse routes ⇒ penalties on arcs of current route (discourage previous routes) ⇒ penalties on adjoined arcs (discourage meandering) quick discovery of diverse routes ⇒ generate lots of new information in each iteration ⇒ speed ⇐ ⇒ quality 24 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  77. Penalty Method penalization (1) requirements enable discovery of diverse routes ⇒ penalties on arcs of current route (discourage previous routes) ⇒ penalties on adjoined arcs (discourage meandering) quick discovery of diverse routes ⇒ generate lots of new information in each iteration ⇒ speed ⇐ ⇒ quality 24 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  78. Penalty Method penalization (1) requirements enable discovery of diverse routes ⇒ penalties on arcs of current route (discourage previous routes) ⇒ penalties on adjoined arcs (discourage meandering) quick discovery of diverse routes ⇒ generate lots of new information in each iteration ⇒ speed ⇐ ⇒ quality 24 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  79. Penalty Method penalization (1) requirements enable discovery of diverse routes ⇒ penalties on arcs of current route (discourage previous routes) ⇒ penalties on adjoined arcs (discourage meandering) quick discovery of diverse routes ⇒ generate lots of new information in each iteration ⇒ speed ⇐ ⇒ quality 24 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  80. Penalty Method penalization (1) requirements enable discovery of diverse routes ⇒ penalties on arcs of current route (discourage previous routes) ⇒ penalties on adjoined arcs (discourage meandering) quick discovery of diverse routes ⇒ generate lots of new information in each iteration ⇒ speed ⇐ ⇒ quality ⇒ how to choose penalty values? 24 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  81. Penalty Method penalization (2) additive penalties (classical method) add fraction of arc/path costs (w.r.t. original metric) ⇒ shortest paths only change slowly geometrically growing penalties (our approach) multiply arc costs on current route by small factor ⇒ often used paths quickly become undesirable add 1 � ( current route cost ) to adjoined arc costs 2 ⇒ discourages short detours on long routes 25 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

  82. Penalty Method penalization (2) additive penalties (classical method) add fraction of arc/path costs (w.r.t. original metric) ⇒ shortest paths only change slowly geometrically growing penalties (our approach) multiply arc costs on current route by small factor ⇒ often used paths quickly become undesirable add 1 � ( current route cost ) to adjoined arc costs 2 ⇒ discourages short detours on long routes 25 Kobitzsch, Radermacher, Schieferdecker: Institute of Theoretical Informatics Evolution and Evaluation of the Penalty Method for Alternative Graphs Algorithmics

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