PACE solver description: tdULL

We describe tdULL, an algorithm for computing treedepth decompositions of minimal depth. An implementation was submitted to the exact track of PACE 2020. tdULL is a branch and bound algorithm branching on inclusion-minimal separators

A flexible and optimal approach for appointment scheduling in healthcare

Appointment scheduling is generally applied in outpatient clinics and other healthcare services. The challenge in scheduling is to find a strategy for dealing with variability and unpredictability in service duration and patient arrivals. The consequences of an ineffective strategy include long waiting times for patients and idle time for the healthcare provider. In turn, these have implications for the perceived quality, cost-efficiency, and capacity of healthcare services. The generation of optimal schedules is a notoriously intractable problem, and earlier attempts at designing effective strategies for appointment scheduling were based on approximation, simulation, or simplification. We propose a novel strategy for scheduling that exploits three tactical ideas to make the problem manageable. We compare the proposed strategy to other approaches, and show that it matches or outperforms competing methods in terms of flexibility, ease of use, and speed. More importantly, it outperforms competing approaches nearly uniformly in approaching the desired balance between waiting and idle times as specified in a chosen objective function. Therefore, the strategy is a good basis for further enrichments

How close does it get?: From near-optimal network algorithms to suboptimal equilibrium outcomes

In this thesis, we first consider a pricing problem of links in networks. We prove inapproximability results and develop approximation algorithms with approximation guarantees that are best possible. Secondly, given a network where each edge has a certain probability of existence, we want to determine the path that has the highest probability of being the shortest path. We prove hardness results and develop a Monte Carlo-type algorithm that, with high probability, returns the correct path. Next, we examine the problem of scheduling jobs on related machines while minimizing the sum of completion times. The approximation guarantee of a simple greedy algorithm is the same as the price of anarchy (PoA) of a game-theoretic version of the problem. We outline a technique that can recover previously known PoA bounds and has the potential to improve them. Further, we analyze the PoA with respect to the social welfare of a first-price auction hosted by a corrupt auctioneer. They approach winning bidders with the offer to lower their bids in return for a fraction of the gains. After obtaining tight robust PoA bounds, we make a no-overbidding assumption, yielding a more fine-grained PoA landscape. Finally, we study the problem of designing truthful mechanisms for players that are (partially) altruistic. We give both a characterization of and a recipe for truthful mechanisms and observe that smaller payments need to be extracted from the players to ensure truthfulness

How close does it get?: From near-optimal network algorithms to suboptimal equilibrium outcomes

In this thesis, we first consider a pricing problem of links in networks. We prove inapproximability results and develop approximation algorithms with approximation guarantees that are best possible. Secondly, given a network where each edge has a certain probability of existence, we want to determine the path that has the highest probability of being the shortest path. We prove hardness results and develop a Monte Carlo-type algorithm that, with high probability, returns the correct path. Next, we examine the problem of scheduling jobs on related machines while minimizing the sum of completion times. The approximation guarantee of a simple greedy algorithm is the same as the price of anarchy (PoA) of a game-theoretic version of the problem. We outline a technique that can recover previously known PoA bounds and has the potential to improve them. Further, we analyze the PoA with respect to the social welfare of a first-price auction hosted by a corrupt auctioneer. They approach winning bidders with the offer to lower their bids in return for a fraction of the gains. After obtaining tight robust PoA bounds, we make a no-overbidding assumption, yielding a more fine-grained PoA landscape. Finally, we study the problem of designing truthful mechanisms for players that are (partially) altruistic. We give both a characterization of and a recipe for truthful mechanisms and observe that smaller payments need to be extracted from the players to ensure truthfulness

A Classification Of Weakly Acyclic Games

International audienceWeakly acyclic games form a natural generalization of the class of games that have the finite improvement property (FIP). In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler recently introduced in [1]