Enumerating Potential Maximal Cliques via SAT and ASP

Peer reviewe

Finding Most Compatible Phylogenetic Trees over Multi-State Characters

Peer reviewe

Finding Optimal Tree Decompositions

The task of organizing a given graph into a structure called a tree decomposition is relevant in multiple areas of computer science. In particular, many NP-hard problems can be solved in polynomial time if a suitable tree decomposition of a graph describing the problem instance is given as a part of the input. This motivates the task of finding as good tree decompositions as possible, or ideally, optimal tree decompositions. This thesis is about finding optimal tree decompositions of graphs with respect to several notions of optimality. Each of the considered notions measures the quality of a tree decomposition in the context of an application. In particular, we consider a total of seven problems that are formulated as finding optimal tree decompositions: treewidth, minimum fill-in, generalized and fractional hypertreewidth, total table size, phylogenetic character compatibility, and treelength. For each of these problems we consider the BT algorithm of Bouchitté and Todinca as the method of finding optimal tree decompositions. The BT algorithm is well-known on the theoretical side, but to our knowledge the first time it was implemented was only recently for the 2nd Parameterized Algorithms and Computational Experiments Challenge (PACE 2017). The author’s implementation of the BT algorithm took the second place in the minimum fill-in track of PACE 2017. In this thesis we review and extend the BT algorithm and our implementation. In particular, we improve the eciency of the algorithm in terms of both theory and practice. We also implement the algorithm for each of the seven problems considered, introducing a novel adaptation of the algorithm for the maximum compatibility problem of phylogenetic characters. Our implementation outperforms alternative state-of-the-art approaches in terms of numbers of test instances solved on well-known benchmarks on minimum fill-in, generalized hypertreewidth, fractional hypertreewidth, total table size, and the maximum compatibility problem of phylogenetic characters. Furthermore, to our understanding the implementation is the first exact approach for the treelength problem

Phasage d’haplotypes par ASP à partir de longues lectures : une approche d’optimisation flexible

Version non corrigée. Une nouvelle version sera disponible d'ici mars 2023.Each chromosome of a di- or polyploid organism has several haplotypes, which are highly similar but diverge on a certain number of positions. However, most of the reference genomes only provide a single sequence for each chromosome, and therefore do not reflect the biological reality.Yet, it is crucial to have access to this information, which is useful in medicine, agronomy and population studies. The recent development of third generation technologies, especially PacBio and Oxford Nanopore Technologies sequencers, has allowed for the production of long reads that facilitate haplotype sequence reconstruction.Bioinformatics methods exist for this task, but they provide only a single solution. This thesis introduces an approach for haplotype phasing based on the search of connected components in a read similarity graph to identify haplotypes. This method uses Answer Set Programming to work on the set ofoptimal solutions. This phasing algorithm has been used to reconstruct haplotypes of the diploid rotifer Adineta vaga.Chaque chromosome d’organisme di- ou polyploïde présente plusieurs haplotypes, qui sont fortement similaires mais divergent sur un certain nombre de positions. Cependant, la majorité des génomes de référence ne renseignent qu’une seule séquence pour chaque chromosome, et ne reflètent donc pas la réalité biologique. Or, il est crucial d’avoir accès à ces informations, qui sont utiles en médecine, en agronomie ou encore dans l’étude des populations. Le récent développement des technologies de troisième génération, notamment des séquenceurs PacBio et Oxford NanoporeTechnologies, a permis la production de lectures longues facilitant la reconstruction des séquences d’haplotypes. Il existe pour cela des méthodes bioinformatiques, mais elles ne fournissent qu’une unique solution. Cette thèse propose une méthode de phasage d’haplotype basée sur la recherchede composantes connexes dans un graph de similarité des lectures pour identifier les haplotypes. Cette méthode utilise l’Answer Set Programming pour travailler sur l’ensemble des solutions optimales. L’algorithme de phasage a permis de reconstruire les haplotypes du rotifère diploïde Adineta vaga

Certifying Correctness for Combinatorial Algorithms : by Using Pseudo-Boolean Reasoning

Over the last decades, dramatic improvements in combinatorialoptimisation algorithms have significantly impacted artificialintelligence, operations research, and other areas. These advances,however, are achieved through highly sophisticated algorithms that aredifficult to verify and prone to implementation errors that can causeincorrect results. A promising approach to detect wrong results is touse certifying algorithms that produce not only the desired output butalso a certificate or proof of correctness of the output. An externaltool can then verify the proof to determine that the given answer isvalid. In the Boolean satisfiability (SAT) community, this concept iswell established in the form of proof logging, which has become thestandard solution for generating trustworthy outputs. The problem isthat there are still some SAT solving techniques for which prooflogging is challenging and not yet used in practice. Additionally,there are many formalisms more expressive than SAT, such as constraintprogramming, various graph problems and maximum satisfiability(MaxSAT), for which efficient proof logging is out of reach forstate-of-the-art techniques.This work develops a new proof system building on the cutting planesproof system and operating on pseudo-Boolean constraints (0-1 linearinequalities). We explain how such machine-verifiable proofs can becreated for various problems, including parity reasoning, symmetry anddominance breaking, constraint programming, subgraph isomorphism andmaximum common subgraph problems, and pseudo-Boolean problems. Weimplement and evaluate the resulting algorithms and a verifier for theproof format, demonstrating that the approach is practical for a widerange of problems. We are optimistic that the proposed proof system issuitable for designing certifying variants of algorithms inpseudo-Boolean optimisation, MaxSAT and beyond

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Assignment Algorithms for Multi-Robot Task Allocation in Uncertain and Dynamic Environments

Multi-robot task allocation is a general approach to coordinate a team of robots to complete a set of tasks collectively. The classical works adopt relevant theories from other disciplines (e.g., operations research, economics), but oftentimes they are not adequately rich to deal with the properties from the robotics domain such as perception that is local and communication which is limited. This dissertation reports the efforts on relaxing the assumptions, making problems simpler and developing new methods considering the constraints or uncertainties in robot problems. We aim to solve variants of classical multi-robot task allocation problems where the team of robots operates in dynamic and uncertain environments. In some of these problems, it is adequate to have a precise model of nondeterministic costs (e.g., time, distance) subject to change at run-time. In some other problems, probabilistic or stochastic approaches are adequate to incorporate uncertainties into the problem formulation. For these settings, we propose algorithms that model dynamics owing to robot interactions, new cost representations incorporating uncertainty, algorithms specialized for the representations, and policies for tasks arriving in an online manner. First, we consider multi-robot task assignment problems where costs for performing tasks are interrelated, and the overall team objective need not be a standard sum-of costs (or utilities) model, enabling straightforward treatment of the additional costs incurred by resource contention. In the model we introduce, a team may choose one of a set of shared resources to perform a task (e.g., several routes to reach a destination), and resource contention is modeled when multiple robots use the same resource. We propose efficient task assignment algorithms that model this contention with different forms of domain knowledge and compute an optimal assignment under such a model. Second, we address the problem of finding the optimal assignment of tasks to a team of robots when the associated costs may vary, which arises when robots deal with uncertain situations. We propose a region-based cost representation incorporating the cost uncertainty and modeling interrelationships among costs. We detail how to compute a sensitivity analysis that characterizes how much costs may change before optimality is violated. Using this analysis, robots are able to avoid unnecessary re-assignment computations and reduce global communication when costs change. Third, we consider multi-robot teams operating in probabilistic domains. We represent costs by distributions capturing the uncertainty in the environment. This representation also incorporates inter-robot couplings in planning the team’s coordination. We do not have the assumption that costs are independent, which is frequently used in probabilistic models. We propose algorithms that help in understanding the effects of different characterizations of cost distributions such as mean and Conditional Value-at-Risk (CVaR), in which the latter assesses the risk of the outcomes from distributions. Last, we study multi-robot task allocation in a setting where tasks are revealed sequentially and where it is possible to execute bundles of tasks. Particularly, we are interested in tasks that have synergies so that the greater the number of tasks executed together, the larger the potential performance gain. We provide an analysis of bundling, giving an understanding of the important bundle size parameter. Based on the qualitative basis, we propose multiple simple bundling policies that determine how many tasks the robots bundle for a batched planning and execution