arXiv subjects

Fanny Pascual

Publications and source records attributed to Fanny Pascual.

6 recordsLinked to original sources

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↗

arXiv2018

Collective Schedules: Scheduling Meets Computational Social Choice

When scheduling public works or events in a shared facility one needs to accommodate preferences of a population. We formalize this problem by introducing the notion of a collective schedule. We show how to extend fundamental tools from social choice theory---positional scoring rules, the Kemeny rule and the Condorcet principle---to collective scheduling. We study the computational complexity of finding collective schedules. We also experimentally demonstrate that optimal collective schedules can be found for instances with realistic sizes.

cs.GT↗

arXiv2018

Two-level lot-sizing with inventory bounds

We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the supply chain so as to satisfy the demands when the quantity of item that can be held in inventory at each period is limited. The inventory bounds can be imposed at the retailer level, at the supplier level or at both levels. We propose a polynomial dynamic programming algorithm to solve this problem when the inventory bounds are set on the retailer level. When the inventory bounds are set on the supplier level, we show that the problem is NP-hard. We give a pseudo-polynomial algorithm which solves this problem when there are inventory bounds on both levels. In the case where demand lot-splitting is not allowed, i.e. each demand has to be satisfied by a single order, we prove that the uncapacitated lot-sizing problem with inventory bounds is strongly NP-hard. This implies that the two-level lot-sizing problems with inventory bounds are also strongly NP-hard when demand lot-splitting is considered.

cs.CC↗

arXiv2017

Optimizing egalitarian performance in the side-effects model of colocation for data center resource management

In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but tasks' performance deteriorates, as colocated tasks compete for shared resources. As tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [18] we proposed a new combinatorial optimization model that uses two parameters of a task - its size and its type - to characterize how a task influences the performance of other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: maximizing the worst-off performance. This problem generalizes the classic makespan minimization on multiple processors (P||Cmax). We prove that polynomially-solvable variants of multiprocessor scheduling are NP-hard and hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics. We simulate the algorithms on instances derived from a trace of one of Google clusters. Algorithms aware of jobs' types lead to better performance compared with algorithms solving P||Cmax. The notion of type enables us to model degeneration of performance caused by using standard combinatorial optimization methods. Types add a layer of additional complexity. However, our results - approximation algorithms and good average-case performance - show that types can be handled efficiently.

cs.DC↗