Island Hopping and Path Colouring Andrew McGregor UPenn UC San - PowerPoint PPT Presentation

Island Hopping and Path Colouring Andrew McGregor UPenn → UC San Diego Bruce Shepherd Bell Labs → McGill

Optical Network Design

Optical Network Design • Route a set of signals, s i to t i , in a graph G

Optical Network Design • Route a set of signals, s i to t i , in a graph G • Advantages of optical communication: A single optical fiber can carry multiple signals if each is assigned a different wavelength. Decreased latency if signals can avoid expensive optical-electrical-optical (OEO) conversions.

Optical Network Design • Route a set of signals, s i to t i , in a graph G • Advantages of optical communication: A single optical fiber can carry multiple signals if each is assigned a different wavelength. Decreased latency if signals can avoid expensive optical-electrical-optical (OEO) conversions. • Many interesting theory problems arise...

Minimizing Fiber Costs

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e .

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e . • MinFiber: Minimize the cost of fibers installed such that every signal can be routed monochromatically.

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e . • MinFiber: Minimize the cost of fibers installed such that every signal can be routed monochromatically. • Approx: O(log n ) and Ω (log 1/4- ε n ) [Andrews, Zhang ’05]

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e . • MinFiber: Minimize the cost of fibers installed such that every signal can be routed monochromatically. • Approx: O(log n ) and Ω (log 1/4- ε n ) [Andrews, Zhang ’05] • Exact solution if G is a path [Winkler, Zhang ’03]

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e . • MinFiber: Minimize the cost of fibers installed such that every signal can be routed monochromatically. • Approx: O(log n ) and Ω (log 1/4- ε n ) [Andrews, Zhang ’05] • Exact solution if G is a path [Winkler, Zhang ’03] • Our results: Exact solution if G is a directed tree and 3.55 approx if demands are single-source.

Minimizing Fiber Costs • In each link e of G , a fiber that can carry a single signal of each wavelength {1, ..., λ } can be installed with cost c e . • MinFiber: Minimize the cost of fibers installed such that every signal can be routed monochromatically. • Approx: O(log n ) and Ω (log 1/4- ε n ) [Andrews, Zhang ’05] • Exact solution if G is a path [Winkler, Zhang ’03] • Our results: Exact solution if G is a directed tree and 3.55 approx if demands are single-source.

Minimizing “Hops”

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers.

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM • Any signal not switched optically requires an OEO conversion or “hop.”

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM • Any signal not switched optically requires an OEO conversion or “hop.” • MinHop c : Given a single infinite capacity fiber in each link, route demands simply and set Roadms to minimize average number of hops.

6 Southgate Loughton Woodside Park 4 Stanmore West Finchley Edgware Minimizing “Hops” Arnos Grove Harrow & 5 Mill Hill East Roding Wealdstone Buckhurst Hill Northwood Burnt Valley Chigwell Finchley Central Canons Park Oak Northwood Bounds Green Hills Colindale East Finchley Wood Green Woodford Queensbury Grange Pinner Hendon Central Hill Highgate Seven Blackhorse North Harrow Kenton Hainault 3 Turnpike Lane Sisters Road Brent Cross Kingsbury 4 • At each node, can only switch signals optically within Harrow- Preston South Fairlop on-the-Hill Road Archway Manor House Woodford Golders Green Tottenham Walthamstow Barkingside Hale Central Newbury West Harrow Northwick Neasden Hampstead Hampstead Gospel Tufnell Park Park Park Heath Oak Wembley Snaresbrook Redbridge Dollis Hill Park South Kenton Arsenal Finsbury Upminster Finchley Road sets of c incident fibers. Kentish South Harrow North Wembley Willesden Green Kentish Holloway Park & Frognal Wanstead Gants Town West Belsize Park Town Road Hill Wembley Central Kilburn Leytonstone Caledonian Road Brondesbury Chalk Farm Stonebridge Park West 3 Park Hampstead Dagenham Harlesden 200m Camden Caledonian Road East Road & Hackney Hackney Camden Town Willesden Junction Leyton Kensal Rise Brondesbury Finchley Road Barnsbury Canonbury Central Wick Kensal Green Swiss Cottage Mornington Highbury & Dagenham Queen’s Park Dalston Homerton St. John’s Wood Crescent King’s Cross Islington Heathway Kingsland St. Pancras Upney Becontree Maida Vale Great 2 Stratford Kilburn Park Portland Edgware Baker Euston Angel Paddington Street Warwick Avenue Road Street Barking Royal Oak Old Street Bethnal Westbourne Park East Ham Euston Warren Street Green Mile End Paddington Edgware Marylebone Farringdon Pudding Square ROADM Upton Park • Any signal not switched optically requires an OEO Regent’s Park Road Liverpool Mill Lane Euston 200m Ladbroke Grove Street Plaistow Bayswater Barbican Shoreditch Russell Latimer Road Bow West Ham Bromley- Square Bow Moorgate Road Goodge by-Bow North White Holland Lancaster Chancery Church Notting Bond Oxford Street Acton City Park Gate Lane 200m Hill Gate Holborn Street Circus 1 2 3 Stepney Green conversion or “hop.” Aldgate Devons Tottenham St. Paul’s 2 West East Shepherd’s Queensway Marble East Whitechapel Road Court Road Acton Acton Bush Arch for Shoreditch Bank Covent Garden All Saints Aldgate Canning Town Acton East Leicester Square 340m High Street Central Hyde Park Green Park Shadwell Westferry India Poplar Kensington Cannon Street Leicester Corner Shepherd’s Kensington • MinHop c : Given a single infinite capacity fiber in each Royal Victoria Mansion Piccadilly Square Bush (Olympia) South House Limehouse Blackwall Circus Monument Custom House Acton Tower Knightsbridge Goldhawk Road Charing for ExCeL London Hill Cross Tower Fenchurch Street 150m West Prince Regent Barons Gloucester Gateway Wapping Blackfriars West India Sloane St. James’s Court Silvertown Hammersmith Road River Thames Quay Royal Albert Square Park link, route demands simply and set Roadms to Temple Rotherhithe Beckton Park London Bridge Canary Wharf Victoria Westminster Embankment Turnham Stamford Ravenscourt West South North Earl’s Pontoon Charing Cross 100m Green Brook Park Kensington Court Kensington Greenwich Canada Dock Bermondsey 2 Water Heron Quays minimize average number of hops. London 1 West Brompton City South Quay Waterloo Airport Gunnersbury Fulham Broadway Silvertown Crossharbour Surrey Quays Parsons Green King Pimlico Southwark Borough Kew Gardens George V Putney Bridge Waterloo East 400m Mudchute North Woolwich River Thames Lambeth North Island Gardens East Putney Richmond Vauxhall Elephant & Castle Southfields 3 Kennington 100m Woolwich Cutty Sark New Cross Gate New Cross Arsenal Wimbledon Park for Maritime Greenwich Greenwich Oval Wimbledon Stockwell Deptford Bridge

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM • Any signal not switched optically requires an OEO conversion or “hop.” • MinHop c : Given a single infinite capacity fiber in each link, route demands simply and set Roadms to minimize average number of hops.

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM • Any signal not switched optically requires an OEO conversion or “hop.” • MinHop c : Given a single infinite capacity fiber in each link, route demands simply and set Roadms to minimize average number of hops. • Approx: O(log n ) and > 2 for c =2 [Anshelevich, Zhang ’05]

Minimizing “Hops” • At each node, can only switch signals optically within sets of c incident fibers. ROADM • Any signal not switched optically requires an OEO conversion or “hop.” • MinHop c : Given a single infinite capacity fiber in each link, route demands simply and set Roadms to minimize average number of hops. • Approx: O(log n ) and > 2 for c =2 [Anshelevich, Zhang ’05] • Our Results: Ω (log 1- ε n ) for c =2...

1. Min-Hop 2. Min-Fiber 3. Min-Both?