35 research outputs found
Efficient parameterized algorithms on structured graphs
In der klassischen KomplexitĂ€tstheorie werden worst-case Laufzeiten von Algorithmen typischerweise einzig abhĂ€ngig von der EingabegröĂe angegeben. In dem Kontext der parametrisierten KomplexitĂ€tstheorie versucht man die Analyse der Laufzeit dahingehend zu verfeinern, dass man zusĂ€tzlich zu der EingabengröĂe noch einen Parameter berĂŒcksichtigt, welcher angibt, wie strukturiert die Eingabe bezĂŒglich einer gewissen Eigenschaft ist. Ein parametrisierter Algorithmus nutzt dann diese beschriebene Struktur aus und erreicht so eine Laufzeit, welche schneller ist als die eines besten unparametrisierten Algorithmus, falls der Parameter klein ist.
Der erste Hauptteil dieser Arbeit fĂŒhrt die Forschung in diese Richtung weiter aus und untersucht den Einfluss von verschieden Parametern auf die Laufzeit von bekannten effizient lösbaren Problemen. Einige vorgestellte Algorithmen sind dabei adaptive Algorithmen, was bedeutet, dass die Laufzeit von diesen Algorithmen mit der Laufzeit des besten unparametrisierten Algorithm fĂŒr den gröĂtmöglichen Parameterwert ĂŒbereinstimmt und damit theoretisch niemals schlechter als die besten unparametrisierten Algorithmen und ĂŒbertreffen diese bereits fĂŒr leicht nichttriviale Parameterwerte.
Motiviert durch den allgemeinen Erfolg und der Vielzahl solcher parametrisierten Algorithmen, welche eine vielzahl verschiedener Strukturen ausnutzen, untersuchen wir im zweiten Hauptteil dieser Arbeit, wie man solche unterschiedliche homogene Strukturen zu mehr heterogenen Strukturen vereinen kann. Ausgehend von algebraischen AusdrĂŒcken, welche benutzt werden können, um von Parametern beschriebene Strukturen zu definieren, charakterisieren wir klar und robust heterogene Strukturen und zeigen exemplarisch, wie sich die Parameter tree-depth und modular-width heterogen verbinden lassen. Wir beschreiben dazu effiziente Algorithmen auf heterogenen Strukturen mit Laufzeiten, welche im Spezialfall mit den homogenen Algorithmen ĂŒbereinstimmen.In classical complexity theory, the worst-case running times of algorithms depend solely on the size of the input. In parameterized complexity the goal is to refine the analysis of the running time of an algorithm by additionally considering a parameter that measures some kind of structure in the input. A parameterized algorithm then utilizes the structure described by the parameter and achieves a running time that is faster than the best general (unparameterized) algorithm for instances of low parameter value.
In the first part of this thesis, we carry forward in this direction and investigate the influence of several parameters on the running times of well-known tractable problems.
Several presented algorithms are adaptive algorithms, meaning that they match the running time of a best unparameterized algorithm for worst-case parameter values. Thus, an adaptive parameterized algorithm is asymptotically never worse than the best unparameterized algorithm, while it outperforms the best general algorithm already for slightly non-trivial parameter values.
As illustrated in the first part of this thesis, for many problems there exist efficient parameterized algorithms regarding multiple parameters, each describing a different kind of structure.
In the second part of this thesis, we explore how to combine such homogeneous structures to more general and heterogeneous structures.
Using algebraic expressions, we define new combined graph classes
of heterogeneous structure in a clean and robust way, and we showcase this for the heterogeneous merge of the parameters tree-depth and modular-width, by presenting parameterized algorithms
on such heterogeneous graph classes and getting running times that match the homogeneous cases throughout
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Space-Efficient Algorithms and Verification Schemes for Graph Streams
Structured data-sets are often easy to represent using graphs. The prevalence of massive data-sets in the modern world gives rise to big graphs such as web graphs, social networks, biological networks, and citation graphs. Most of these graphs keep growing continuously and pose two major challenges in their processing: (a) it is infeasible to store them entirely in the memory of a regular server, and (b) even if stored entirely, it is incredibly inefficient to reread the whole graph every time a new query appears. Thus, a natural approach for efficiently processing and analyzing such graphs is reading them as a stream of edge insertions and deletions and maintaining a summary that can be (a) stored in affordable memory (significantly smaller than the input size) and (b) used to detect properties of the original graph. In this thesis, we explore the strengths and limitations of such graph streaming algorithms under three main paradigms: classical or standard streaming, adversarially robust streaming, and streaming verification.
In the classical streaming model, an algorithm needs to process an adversarially chosen input stream using space sublinear in the input size and return a desired output at the end of the stream. Here, we study a collection of fundamental directed graph problems like reachability, acyclicity testing, and topological sorting. Our investigation reveals that while most problems are provably hard for general digraphs, they admit efficient algorithms for the special and widely-studied subclass of tournament graphs. Further, we exhibit certain problems that become drastically easier when the stream elements arrive in random order rather than adversarial order, as well as problems that do not get much easier even under this relaxation. Furthermore, we study the graph coloring problem in this model and design color-efficient algorithms using novel parameterizations and establish complexity separations between different versions of the problem.
The classical streaming setting assumes that the entire input stream is fixed by an adversary before the algorithm reads it. Many randomized algorithms in this setting, however, fail when the stream is extended by an adaptive adversary based on past outputs received. This is the so-called adversarially robust streaming model. We show that graph coloring is significantly harder in the robust setting than in the classical setting, thus establishing the first such separation for a ``natural\u27\u27 problem. We also design a class of efficient robust coloring algorithms using novel techniques.
In classical streaming, many important problems turn out to be ``intractable\u27\u27, i.e., provably impossible to solve in sublinear space. It is then natural to consider an enhanced streaming setting where a space-bounded client outsources the computation to a space-unbounded but untrusted cloud service, who replies with the solution and a supporting ``proof\u27\u27 that the client needs to verify. This is called streaming verification or the annotated streaming model. It allows algorithms or verification schemes for the otherwise intractable problems using both space and proof length sublinear in the input size. We devise efficient schemes that improve upon the state of the art for a variety of fundamental graph problems including triangle counting, maximum matching, topological sorting, maximal independent set, graph connectivity, and shortest paths, as well as for computing frequency-based functions such as distinct items and maximum frequency, which have broad applications in graph streaming. Some of our schemes were conjectured to be impossible, while some others attain smooth and optimal tradeoffs between space and communication costs
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
Sublinear Algorithm And Lower Bound For Combinatorial Problems
As the scale of the problems we want to solve in real life becomes larger, the input sizes of the problems we want to solve could be much larger than the memory of a single computer. In these cases, the classical algorithms may no longer be feasible options, even when they run in linear time and linear space, as the input size is too large.
In this thesis, we study various combinatorial problems in different computation models that process large input sizes using limited resources. In particular, we consider the query model, streaming model, and massively parallel computation model. In addition, we also study the tradeoffs between the adaptivity and performance of algorithms in these models.We first consider two graph problems, vertex coloring problem and metric traveling salesman problem (TSP). The main results are structure results for these problems, which give frameworks for achieving sublinear algorithms of these problems in different models. We also show that the sublinear algorithms for (â + 1)-coloring problem are tight. We then consider the graph sparsification problem, which is an important technique for designing sublinear algorithms. We give proof of the existence of a linear size hypergraph cut sparsifier, along with a polynomial algorithm that calculates one. We also consider sublinear algorithms for this problem in the streaming and query models. Finally, we study the round complexity of submodular function minimization (SFM). In particular, we give a polynomial lower bound on the number of rounds we need to compute s â t max flow - a special case of SFM - in the streaming model. We also prove a polynomial lower bound on the number of rounds we need to solve the general SFM problem in polynomial queries
13th International Conference on Modeling, Optimization and Simulation - MOSIM 2020
ComitĂ© dâorganisation: UniversitĂ© Internationale dâAgadir â Agadir (Maroc) Laboratoire Conception Fabrication Commande â Metz (France)Session RS-1 âSimulation et Optimisationâ / âSimulation and Optimizationâ Session RS-2 âPlanification des Besoins MatiĂšres PilotĂ©e par la Demandeâ / âDemand-Driven Material Requirements Planningâ Session RS-3 âIngĂ©nierie de SystĂšmes BasĂ©es sur les ModĂšlesâ / âModel-Based System Engineeringâ Session RS-4 âRecherche OpĂ©rationnelle en Gestion de Productionâ / "Operations Research in Production Management" Session RS-5 "Planification des MatiĂšres et des Ressources / Planification de la Productionâ / âMaterial and Resource Planning / Production Planning" Session RS-6 âMaintenance Industrielleâ / âIndustrial Maintenanceâ Session RS-7 "Etudes de Cas Industrielsâ / âIndustrial Case Studies" Session RS-8 "DonnĂ©es de Masse / Analyse de DonnĂ©esâ / âBig Data / Data Analytics" Session RS-9 "Gestion des SystĂšmes de Transportâ / âTransportation System Management" Session RS-10 "Economie Circulaire / DĂ©veloppement Durable" / "Circular Economie / Sustainable Development" Session RS-11 "Conception et Gestion des ChaĂźnes Logistiquesâ / âSupply Chain Design and Management" Session SP-1 âIntelligence Artificielle & Analyse de DonnĂ©es pour la Production 4.0â / âArtificial Intelligence & Data Analytics in Manufacturing 4.0â Session SP-2 âGestion des Risques en Logistiqueâ / âRisk Management in Logisticsâ Session SP-3 âGestion des Risques et Evaluation de Performanceâ / âRisk Management and Performance Assessmentâ Session SP-4 "Indicateurs ClĂ©s de Performance 4.0 et Dynamique de Prise de DĂ©cisionâ / â4.0 Key Performance Indicators and Decision-Making Dynamics" Session SP-5 "Logistique Maritimeâ / âMarine Logistics" Session SP-6 âTerritoire et Logistique : Un SystĂšme Complexeâ / âTerritory and Logistics: A Complex Systemâ Session SP-7 "Nouvelles AvancĂ©es et Applications de la Logique Floue en Production Durable et en Logistiqueâ / âRecent Advances and Fuzzy-Logic Applications in Sustainable Manufacturing and Logistics" Session SP-8 âGestion des Soins de SantĂ©â / âHealth Care Managementâ Session SP-9 âIngĂ©nierie Organisationnelle et Gestion de la ContinuitĂ© de Service des SystĂšmes de SantĂ© dans lâEre de la Transformation NumĂ©rique de la SociĂ©tĂ©â / âOrganizational Engineering and Management of Business Continuity of Healthcare Systems in the Era of Numerical Society Transformationâ Session SP-10 âPlanification et Commande de la Production pour lâIndustrie 4.0â / âProduction Planning and Control for Industry 4.0â Session SP-11 âOptimisation des SystĂšmes de Production dans le Contexte 4.0 Utilisant lâAmĂ©lioration Continueâ / âProduction System Optimization in 4.0 Context Using Continuous Improvementâ Session SP-12 âDĂ©fis pour la Conception des SystĂšmes de Production Cyber-Physiquesâ / âChallenges for the Design of Cyber Physical Production Systemsâ Session SP-13 âProduction AvisĂ©e et DĂ©veloppement Durableâ / âSmart Manufacturing and Sustainable Developmentâ Session SP-14 âLâHumain dans lâUsine du Futurâ / âHuman in the Factory of the Futureâ Session SP-15 âOrdonnancement et PrĂ©vision de ChaĂźnes Logistiques RĂ©silientesâ / âScheduling and Forecasting for Resilient Supply Chains
Computer Aided Verification
This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency