arXiv subjects

Martin Durand

Publications and source records attributed to Martin Durand.

7 recordsLinked to original sources

arXiv2026

Finding Low Star Discrepancy 3D Kronecker Point Sets Using Algorithm Configuration Techniques

The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for quasi-Monte Carlo integration methods, and many other applications. Recent work has shown that classical constructions such as Sobol', Halton, or Hammersley sequences can be outperformed by large margins when considering point sets of fixed sizes rather than their convergence behavior. These results, highly relevant to the aforementioned applications, raise the question of how much existing constructions can be improved through size-specific optimization. In this work, we study this question for the so-called Kronecker construction. Focusing on the 3-dimensional setting, we show that optimizing the two configurable parameters of its construction yields point sets outperforming the state-of-the-art value for sets of at least 500 points. Using the algorithm configuration technique irace, we then derive parameters that yield new state-of-the-art discrepancy values for whole ranges of set sizes.

cs.NE↗

arXiv2026

Two NP-hard Extensions of the Spearman Footrule even for a Small Constant Number of Voters

The Spearman footrule is a voting rule that takes as input voter preferences expressed as rankings. It outputs a ranking that minimizes the sum of the absolute differences between the position of each candidate in the ranking and in the voters' preferences. In this paper, we study the computational complexity of two extensions of the Spearman footrule when the number of voters is a small constant. The first extension, introduced by Pascual et al. (2018), arises from the collective scheduling problem and treats candidates, referred to as tasks in their model, as having associated lengths. The second extension, proposed by Kumar and Vassilvitskii (2010), assigns weights to candidates; these weights serve both as lengths, as in the collective scheduling model, and as coefficients in the objective function to be minimized. Although computing a ranking under the standard Spearman footrule is polynomial-time solvable, we demonstrate that the first extension is NP-hard with as few as 3 voters, and the second extension is NP-hard with as few as 4 voters. Both extensions are polynomial-time solvable for 2 voters.

cs.CC↗

arXiv2025

Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity

We investigate multi-organizational scheduling problems, building upon the framework introduced by Pascual et al.[2009]. In this setting, multiple organizations each own a set of identical machines and sequential jobs with distinct processing times. The challenge lies in optimally assigning jobs across organizations' machines to minimize the overall makespan while ensuring no organization's performance deteriorates. To formalize this fairness constraint, we introduce individual rationality, a game-theoretic concept that guarantees each organization benefits from participation. Our analysis reveals that finding an individually rational schedule with minimum makespan is $\Theta_2^{\text{P}}$-hard, placing it in a complexity class strictly harder than both NP and coNP. We further extend the model by considering an alternative objective: minimizing the sum of job completion times, both within individual organizations and across the entire system. The corresponding decision variant proves to be NP-complete. Through comprehensive parameterized complexity analysis of both problems, we provide new insights into these computationally challenging multi-organizational scheduling scenarios.

cs.GT↗

arXiv2025

Parameterized Complexity of Hedonic Games with Enemy-Oriented Preferences

Hedonic games model settings in which a set of agents have to be partitioned into groups which we call coalitions. In the enemy aversion model, each agent has friends and enemies, and an agent prefers to be in a coalition with as few enemies as possible and, subject to that, as many friends as possible. A partition should be stable, i.e., no subset of agents prefer to be together rather than being in their assigned coalition under the partition. We look at two stability concepts: core stability and strict core stability. This yields several algorithmic problems: determining whether a (strictly) core stable partition exists, finding such a partition, and checking whether a given partition is (strictly) core stable. Several of these problems have been shown to be NP-complete, or even beyond NP. This motivates the study of parameterized complexity. We conduct a thorough computational study using several parameters: treewidth, number of friends, number of enemies, partition size, and coalition size. We give polynomial algorithms for restricted graph classes as well as FPT algorithms with respect to the number of friends an agent may have and the treewidth of the graph representing the friendship or enemy relations. We show W[1]-hardness or para-NP-hardness with respect to the other parameters. We conclude this paper with results in the setting in which agents can have neutral relations with each other, including hardness-results for very restricted cases.

cs.GT↗

arXiv2024

Detecting and taking Project Interactions into account in Participatory Budgeting

The aim of this paper is to introduce models and algorithms for the Participatory Budgeting problem when projects can interact with each other. In this problem, the objective is to select a set of projects that fits in a given budget. Voters express their preferences over the projects and the goal is then to find a consensus set of projects that does not exceed the budget. Our goal is to detect such interactions thanks to the preferences expressed by the voters. Through the projects selected by the voters, we detect positive and negative interactions between the projects by identifying projects that are consistently chosen together. In presence of project interactions, it is preferable to select projects that interact positively rather than negatively, all other things being equal. We introduce desirable properties that utility functions should have in presence of project interactions and we build a utility function which fulfills the desirable properties introduced. We then give axiomatic properties of aggregation rules, and we study three classical aggregation rules: the maximization of the sum of the utilities, of the product of the utilities, or of the minimal utility. We show that in the three cases the problems solved by these rules are NP-hard, and we propose a branch and bound algorithm to solve them. We conclude the paper by experiments.

cs.GT↗

arXiv2024

Ordering Collective Unit Tasks: from Scheduling to Computational Social Choice

We study the collective schedules problem, which consists in computing a one machine schedule of a set of tasks, knowing that a set of individuals (also called voters) have preferences regarding the order of the execution of the tasks. Our aim is to return a consensus schedule. We consider the setting in which all tasks have the same length -- such a schedule can therefore also be viewed as a ranking. We study two rules, one based on a distance criterion, and another one based one a binary criterion, and we show that these rules extend classic scheduling criteria. We also consider time constraints and precedence constraints between the tasks, and focus on two cases: the preferences of the voters fulfill these constraints, or they do not fulfill these constraints (but the collective schedule should fulfill them). In each case, either we show that the problem is NP-hard, or we provide a polynomial time algorithm which solves it. We also provide an analysis of a heuristic, which appears to be a 2 approximation of the Spearman's rule.

cs.GT↗

arXiv2024

Collective schedules: axioms and algorithms

The collective schedules problem consists in computing a schedule of tasks shared between individuals. Tasks may have different duration, and individuals have preferences over the order of the shared tasks. This problem has numerous applications since tasks may model public infrastructure projects, events taking place in a shared room, or work done by co-workers. Our aim is, given the preferred schedules of individuals (voters), to return a consensus schedule. We propose an axiomatic study of the collective schedule problem, by using classic axioms in computational social choice and new axioms that take into account the duration of the tasks. We show that some axioms are incompatible, and we study the axioms fulfilled by three rules: one which has been studied in the seminal paper on collective schedules (Pascual et al. 2018), one which generalizes the Kemeny rule, and one which generalizes Spearman's footrule. From an algorithmic point of view, we show that these rules solve NP-hard problems, but that it is possible to solve optimally these problems for small but realistic size instances, and we give an efficient heuristic for large instances. We conclude this paper with experiments.

cs.GT↗