Evripidis Bampis’s research while affiliated with French National Centre for Scientific Research and other places

We consider a learning-augmented framework for NP-hard permutation problems. The algorithm has access to predictions telling, given a pair u,v of elements, whether u is before v or not in an optimal solution. Building on the work of Braverman and Mossel (SODA 2008), we show that for a class of optimization problems including scheduling, network design and other graph permutation problems, these predictions allow to solve them in polynomial time with high probability, provided that predictions are true with probability at least $1/2+\epsilon$. Moreover, this can be achieved with a parsimonious access to the predictions.

We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.

In the Traveling Salesperson Problem (TSP) we are given a list of locations and the distances between each pair of them. The goal is to find the shortest possible tour that visits each location exactly once and returns to the starting location. Inspired by the fact that general TSP cannot be approximated in polynomial time within any constant factor, while metric TSP admits a (slightly better than) 1.5-approximation in polynomial time, Zhou, Li and Guo [Zhou et al., ISAAC '22] introduced a parameter that measures the distance of a given TSP instance from the metric case. They gave an FPT 3-approximation algorithm parameterized by k, where k is the number of triangles in which the edge costs violate the triangle inequality. In this paper, we design a 2.5-approximation algorithm that runs in FPT time, improving the result of [Zhou et al., ISAAC '22].

In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to return to the origin when all the requests are served, as well as the closed variant, in which the algorithm has to return to the origin after serving all the requests. Our aim is to measure the impact of the extra knowledge of the locations on the competitiveness of the problem. We present an online 3/2-competitive algorithm for the general case and a matching lower bound for both the open and the closed variant. Then, we focus on some interesting metric spaces (ring, star, semi-line), providing both lower bounds and polynomial time online algorithms for the problem.KeywordsTSPOnline algorithmsCompetitive analysis

We study the Online Traveling Salesperson Problem (OLTSP) with predictions. In OLTSP, a sequence of initially unknown requests arrive over time at points (locations) of a metric space. The goal is, starting from a particular point of the metric space (the origin), to serve all these requests while minimizing the total time spent. The server moves with unit speed or is "waiting" (zero speed) at some location. We consider two variants: in the open variant, the goal is achieved when the last request is served. In the closed one, the server additionally has to return to the origin. We adopt a prediction model, introduced for OLTSP on the line, in which the predictions correspond to the locations of the requests and extend it to more general metric spaces. We first propose an oracle-based algorithmic framework, inspired by previous work. This framework allows us to design online algorithms for general metric spaces that provide competitive ratio guarantees which, given perfect predictions, beat the best possible classical guarantee (consistency). Moreover, they degrade gracefully along with the increase in error (smoothness), but always within a constant factor of the best known competitive ratio in the classical case (robustness). Having reduced the problem to designing suitable efficient oracles, we describe how to achieve this for general metric spaces as well as specific metric spaces (rings, trees and flowers), the resulting algorithms being tractable in the latter case. The consistency guarantees of our algorithms are tight in almost all cases, and their smoothness guarantees only suffer a linear dependency on the error, which we show is necessary. Finally, we provide robustness guarantees improving previous results.

Cet article propose une nouvelle perspective d’étude de la carte électorale, fondée sur la computational social science, pour analyser les critères qui encadrent la réalisation du découpage électoral en France. La délimitation des circonscriptions législatives est complexe en raison de sa dimension technique et des critères juridiques, démographiques et géographiques à respecter. À partir des données démographiques et géographiques des territoires et de la mesure de l’ensemble des découpages admissibles, nous évaluons les contraintes formées par les critères sur les potentialités empiriques de la carte électorale et, plus largement, nous montrons l’intérêt d’avoir recours aux découpages assistés par ordinateur. ------ This article proposes a new perspective for understanding electoral maps, using computational social science to study the criteria which shape how electoral districts are drawn up in France. Defining the boundaries of legislative constituencies is a complex task, given its technical dimension and the various demographic, geographic, and legal criteria that must be respected. Looking at demographic and geographic territorial data and the whole of the admissible redistrictings, we evaluate the criteria-based constraints on the empirical possibilities of the electoral map and, more broadly, we highlight the value of using computer for the map making of the electoral constituencies redistricting.

In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to return to the origin when all the requests are served, as well as the closed variant, in which the algorithm has to return to the origin after serving all the requests. Our aim is to measure the impact of the extra knowledge of the locations on the competitiveness of the problem. We present an online 3/2-competitive algorithm for the general case and a matching lower bound for both the open and the closed variant. Then, we focus on some interesting metric spaces (ring, star, semi-line), providing both lower bounds and polynomial time online algorithms for the problem.

In this work, we consider the k-Canadian Traveller Problem (k-CTP) under the learning-augmented framework proposed by Lykouris & Vassilvitskii [23]. k-CTP is a generalization of the shortest path problem, and involves a traveller who knows the entire graph in advance and wishes to find the shortest route from a source vertex s to a destination vertex t, but discovers online that some edges (up to k) are blocked once reaching them. A potentially imperfect predictor gives us the number and the locations of the blocked edges.We present a deterministic and a randomized online algorithm for the learning-augmented k-CTP that achieve a tradeoff between consistency (quality of the solution when the prediction is correct) and robustness (quality of the solution when there are errors in the prediction). Moreover, we prove a matching lower bound for the deterministic case establishing that the tradeoff between consistency and robustness is optimal, and show a lower bound for the randomized algorithm. Finally, we prove several deterministic and randomized lower bounds on the competitive ratio of k-CTP depending on the prediction error, and complement them, in most cases, with matching upper bounds.KeywordsCanadian Traveller ProblemOnline algorithmLearning augmented algorithm