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

Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions

Thomas Kesselheim1 Andreas T¨

• nnis2

1Department of Computer Science - TU Dortmund, Germany 2Department of Computer Science - University of Bonn, Germany

June 10, 2017

Kesselheim and T¨

• nnis

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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¨

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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 10 years

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The Temp Secretary Problem

Fiat et al. [ESA’15]

Example: γ = 0.2 and B = 1

0.5 1

Weight wj for each candidate j Arrival date τj ∈ [0, 1] uniformly at random Contract durations γ Temporal packing constraints, e.g. ≤ B candidates at a time Objective: max

j∈S wj

Kesselheim and T¨

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The Temp Secretary Problem

Fiat et al. [ESA’15]

Example: γ = 0.2 and B = 1

5 2 6 3 13 7 15 12 5 8 10 0.5 1

Choice: 5 + 8 + 12 + 13 = 38 Weight wj for each candidate j Arrival date τj ∈ [0, 1] uniformly at random Contract durations γ Temporal packing constraints, e.g. ≤ B candidates at a time Objective: max

j∈S wj

Kesselheim and T¨

• nnis

Temp Secretary Algorithms June 10, 2017 3 / 6

The Temp Secretary Problem

Fiat et al. [ESA’15]

Example: γ = 0.2 and B = 1

5 2 6 3 13 7 15 12 5 8 10 0.5 1

Choice: 5 + 8 + 12 + 13 = 38 Opt.: 7 + 15 + 12 + 13 = 45 Weight wj for each candidate j Arrival date τj ∈ [0, 1] uniformly at random Contract durations γ Temporal packing constraints, e.g. ≤ B candidates at a time Objective: max

j∈S wj

Kesselheim and T¨

• nnis

Temp Secretary Algorithms June 10, 2017 3 / 6

The Temp Secretary Problem

Fiat et al. [ESA’15]

Example: γ = 0.2 and B = 1

5 2 6 3 13 7 15 12 5 8 10 0.5 1

Choice: 5 + 8 + 12 + 13 = 38 Opt.: 7 + 15 + 12 + 13 = 45 Weight wj for each candidate j Arrival date τj ∈ [0, 1] uniformly at random Contract durations γ Temporal packing constraints, e.g. ≤ B candidates at a time Objective: max

j∈S wj

Here OPT(I) is a random variable c-competitive if E [ALG(I)] ≥ c · E [OPT(I)]

Kesselheim and T¨

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Our Results

We give a simple algorithm for the problem with γ ≪ 1 that is

1 2 − O(√γ)-competitive for all B

1 − O( 1

√ B ) − O(√γ)-competitive for large B

Generalizations linear packing constraints

1 4 − O(√γ)-competitive for different lengths λj ≤ γ and B = 1

Kesselheim and T¨

• nnis

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A Non-Temporal Relaxation

For every feasible selection of candidates holds: at most B candidates selected within last γ time interval ⇒ at most B

• 1

γ

• candidates selected in total

Kesselheim and T¨

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A Non-Temporal Relaxation

For every feasible selection of candidates holds: at most B candidates selected within last γ time interval ⇒ at most B

• 1

γ

• candidates selected in total

Idea: spread selections evenly over arrival interval

Linear Scaling Approach

Attempt selection of candidate j if the candidate is within the

• τj B

γ

• best

candidates seen so far.

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Details...

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Details...

I am happy to discuss details at the poster!

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