Showing papers by "Barry O'Sullivan published in 2018"

Three-dimensional matching instances are rich in stable matchings

Abstract: Extensive studies have been carried out on the Stable Matching problem, but they mostly consider cases where the agents to match belong to either one or two sets. Little work has been done on the three-set extension, despite the many applications in which three-dimensional stable matching (3DSM) can be used. In this paper we study the Cyclic 3DSM problem, a variant of 3DSM where agents in each set only rank the agents from one other set, in a cyclical manner. The question of whether every Cyclic 3DSM instance admits a stable matching has remained open for many years. We give the exact number of stable matchings for the class of Cyclic 3DSM instances where all agents in the same set share the same master preference list. This number is exponential in the size of the instances. We also show through empirical experiments that this particular class contains the most constrained Cyclic 3DSM instances, the ones with the fewest stable matchings. This would suggest that not only do all Cyclic 3DSM instances have at least one stable matching, but they each have an exponential number of them.

From Offline to Online Kidney Exchange Optimization

Abstract: Kidney exchange programs enable willing, but incompatible, donor-patient pairs to swap donors, thus allowing persons suffering from organ failure to access transplantation. Choosing which pairs to match requires solving a stochastic online optimization problem where patients and donors arrive over time. Despite this, most of the related scientific literature has focused on deterministic offline models. In this paper, we present a simple approach to employ a model for the offline Kidney Exchange Problem (KEP) as the basis of an on-line anticipatory algorithm. Our approach grounds on existing techniques for the on-line KEP, but it generalizes them and provides a more accurate estimate of the expected impact of current decisions. In an experimentation based on a state-of-the-art donor pool generation method, the approach provides improvements in terms of quality and is able to deal with realistic instance size in reasonable time.

Assigning and Scheduling Service Visits in a Mixed Urban/Rural Setting

Abstract: In this paper we describe a complex optimization application arising in maintenance scheduling, developed in close collaboration with an industrial partner. We have to plan and schedule preventive and corrective maintenance activities at customer sites by a group of traveling repair technicians. A specific property of the problem considered here is a mix of customers in both urban centers and rural areas. This means that travel times between customers must be considered when balancing overall workload for each agent. We discuss a problem decomposition compatible with current management practice, describe different solvers for the individual problem steps, and show results on real-world data from the industrial partner.

A constraint-based parallel local search for the edge-disjoint rooted distance-constrained minimum spanning tree problem

Abstract: Many network design problems arising in areas as diverse as VLSI circuit design, QoS routing, traffic engineering, and computational sustainability require clients to be connected to a facility under path-length constraints and budget limits. These problems can be seen as instances of the rooted distance-constrained minimum spanning-tree problem (RDCMST), which is NP-hard. An inherent feature of these networks is that they are vulnerable to a failure. Therefore, it is often important to ensure that all clients are connected to two or more facilities via edge-disjoint paths. We call this problem the edge-disjoint RDCMST (ERDCMST). Previous work on the RDCMST has focused on dedicated algorithms and therefore it is difficult to use these algorithms to tackle the ERDCMST. We present a constraint-based parallel local search algorithm for solving the ERDCMST. Traditional ways of extending a sequential algorithm to run in parallel perform either portfolio-based search in parallel or parallel neighbourhood search. Instead, we exploit the semantics of the constraints of the problem to perform multiple moves in parallel by ensuring that they are mutually independent. The ideas presented in this paper are general and can be adapted to other problems as well. The effectiveness of our approach is demonstrated by experimenting with a set of problem instances taken from real-world passive optical network deployments in Ireland, Italy, and the UK. Our results show that performing moves in parallel can significantly reduce the elapsed time and improve the quality of the solutions of our local search approach.

Parallel Constraint-Based Local Search: An Application to Designing Resilient Long-Reach Passive Optical Networks

Abstract: Many network design problems arising in areas as diverse as VLSI circuit design, QoS routing, traffic engineering, and computational sustainability require clients to be connected to a facility under path-length constraints and budget limits. These problems can be seen as instances of the Rooted Distance-Constrained Minimum Spanning-Tree problem (RDCMST), which is NP-hard. An inherent feature of these networks is that they are vulnerable to a failure. Therefore, it is often important to ensure that all clients are connected to two or more facilities via edge-disjoint paths.We call this problem the Edge-disjoint RDCMST (ERDCMST). Previous work on RDCMST has focused on dedicated algorithms and, therefore, it is difficult to use these algorithms to tackle ERDCMST. We present a constraint-based parallel local search algorithm for solving ERDCMST. Traditional ways of extending a sequential algorithm to run in parallel perform either portfolio-based search in parallel or parallel neighbourhood search. Instead, we exploit the semantics of the constraints of the problem to perform multiple moves in parallel by ensuring that they are mutually independent. The ideas presented in this chapter are general and can be adapted to other problems as well. The effectiveness of our approach is demonstrated by experimenting with a set of problem instances taken from real-world passive optical network deployments in Ireland, Italy, and the UK. Our results show that performing moves in parallel can significantly reduce the elapsed time and improve the quality of the solutions of our local search approach.

From backdoor key to backdoor completability: improving a known measure of hardness for the satisfiable CSP

Abstract: Many studies have been conducted on the complexity of Constraint Satisfaction Problem (CSP) classes. However, there exists little theoretical work on the hardness of individual CSP instances. In this context, the backdoor key fraction (BKF) [17] was introduced as a quantifier of problem hardness for individual satisfiable instances with regard to backtracking search. In our paper, after highlighting the weaknesses of the BKF, we propose a better characterization of the hardness of an individual satisfiable CSP instance based on the ratio between the size of the solution space and that of the search space. We formally show that our measure is negatively correlated with instance hardness. We also show through experiments that this measure evaluates more accurately the hardness of individual instances than the BKF.

Constrainedness in Stable Matching

Abstract: In constraint satisfaction problems, constrainedness provides a way to predict the number of solutions: for instances of a same size, the number of constraints is inversely correlated with the number of solutions. However, there is no obvious equivalent metric for stable matching problems. We introduce the contrarian score, a simple metric that is to matching problems what constrainedness is to constraint satisfaction problems. In addition to comparing the contrarian score against other potential tightness metrics, we test it for different instance sizes as well as extremely distinct versions of the stable matching problem. In all cases, we find that the correlation between contrarian score and number of solutions is very strong.