Think Eternally: Improved Algorithms for the Temp Secretary Problem - PowerPoint PPT Presentation

Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions Thomas Kesselheim 1 Andreas T¨ onnis 2 1 Department of Computer Science - TU Dortmund, Germany 2 Department of Computer Science - University of Bonn, Germany June 10, 2017 Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 1 / 6

Motivation: Hiring with Fixed-Term Contracts Classical secretary problem often motivated with a hiring process Now, limited time horizon and fixed-term contracts Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 2 / 6

Motivation: Hiring with Fixed-Term Contracts Classical secretary problem often motivated with a hiring process Now, limited time horizon and fixed-term contracts E.g. 10 years project, 1 position and 2 year contracts � � � � � � 5 years 0 10 years Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 2 / 6

The Temp Secretary Problem Fiat et al. [ESA’15] Example: γ = 0 . 2 and B = 1 Weight w j for each candidate j Arrival date τ j ∈ [0 , 1] uniformly at random Contract durations γ Temporal packing constraints, 0 . 5 0 1 e.g. ≤ B candidates at a time Objective: max � j ∈ S w j Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 3 / 6

The Temp Secretary Problem Fiat et al. [ESA’15] Example: γ = 0 . 2 and B = 1 Weight w j for each candidate j 8 10 Arrival date τ j ∈ [0 , 1] uniformly at random 7 15 12 5 Contract durations γ 5 2 6 3 13 Temporal packing constraints, 0 . 5 0 1 e.g. ≤ B candidates at a time Choice: 5 + 8 + 12 + 13 = 38 Objective: max � j ∈ S w j Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 3 / 6

The Temp Secretary Problem Fiat et al. [ESA’15] Example: γ = 0 . 2 and B = 1 Weight w j for each candidate j 8 10 Arrival date τ j ∈ [0 , 1] uniformly at random 7 15 12 5 Contract durations γ 5 2 6 3 13 Temporal packing constraints, 0 . 5 0 1 e.g. ≤ B candidates at a time Choice: 5 + 8 + 12 + 13 = 38 Objective: max � j ∈ S w j Opt.: 7 + 15 + 12 + 13 = 45 Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 3 / 6

The Temp Secretary Problem Fiat et al. [ESA’15] Example: γ = 0 . 2 and B = 1 Weight w j for each candidate j 8 10 Arrival date τ j ∈ [0 , 1] uniformly at random 7 15 12 5 Contract durations γ 5 2 6 3 13 Temporal packing constraints, 0 . 5 0 1 e.g. ≤ B candidates at a time Choice: 5 + 8 + 12 + 13 = 38 Objective: max � j ∈ S w j Opt.: 7 + 15 + 12 + 13 = 45 Here OPT ( I ) is a random variable c -competitive if E [ALG( I )] ≥ c · E [OPT( I )] Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 3 / 6

Our Results We give a simple algorithm for the problem with γ ≪ 1 that is 2 − O ( √ γ )-competitive for all B 1 B ) − O ( √ γ )-competitive for large B 1 − O ( 1 √ Generalizations linear packing constraints 4 − O ( √ γ )-competitive for different lengths λ j ≤ γ and B = 1 1 Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 4 / 6

A Non-Temporal Relaxation For every feasible selection of candidates holds: at most B candidates selected within last γ time interval � � 1 ⇒ at most B candidates selected in total γ Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 5 / 6

A Non-Temporal Relaxation For every feasible selection of candidates holds: at most B candidates selected within last γ time interval � � 1 ⇒ at most B candidates selected in total γ Idea: spread selections evenly over arrival interval Linear Scaling Approach � � τ j B Attempt selection of candidate j if the candidate is within the best γ candidates seen so far. Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 5 / 6

Details... Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 6 / 6

Details... I am happy to discuss details at the poster! Kesselheim and T¨ onnis Temp Secretary Algorithms June 10, 2017 6 / 6