14 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Traveling Salesman Problem

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    The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    29th International Symposium on Algorithms and Computation: ISAAC 2018, December 16-19, 2018, Jiaoxi, Yilan, Taiwan

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    On Flows, Paths, Roots, and Zeros

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    This thesis has two parts; in the first of which we give new results for various network flow problems. (1) We present a novel dual ascent algorithm for min-cost flow and show that an implementation of it is very efficient on certain instance classes. (2) We approach the problem of numerical stability of interior point network flow algorithms by giving a path following method that works with integer arithmetic solely and is thus guaranteed to be free of any nu-merical instabilities. (3) We present a gradient descent approach for the undirected transship-ment problem and its special case, the single source shortest path problem (SSSP). For distrib-uted computation models this yields the first SSSP-algorithm with near-optimal number of communication rounds. The second part deals with fundamental topics from algebraic computation. (1) We give an algorithm for computing the complex roots of a complex polynomial. While achieving a com-parable bit complexity as previous best results, our algorithm is simple and promising to be of practical impact. It uses a test for counting the roots of a polynomial in a region that is based on Pellet's theorem. (2) We extend this test to polynomial systems, i.e., we develop an algorithm that can certify the existence of a k-fold zero of a zero-dimensional polynomial system within a given region. For bivariate systems, we show experimentally that this approach yields signifi-cant improvements when used as inclusion predicate in an elimination method.Im ersten Teil dieser Dissertation präsentieren wir neue Resultate für verschiedene Netzwerkflussprobleme. (1)Wir geben eine neue Duale-Aufstiegsmethode für das Min-Cost-Flow- Problem an und zeigen, dass eine Implementierung dieser Methode sehr effizient auf gewissen Instanzklassen ist. (2)Wir behandeln numerische Stabilität von Innere-Punkte-Methoden fürNetwerkflüsse, indem wir eine solche Methode angeben die mit ganzzahliger Arithmetik arbeitet und daher garantiert frei von numerischen Instabilitäten ist. (3) Wir präsentieren ein Gradienten-Abstiegsverfahren für das ungerichtete Transshipment-Problem, und seinen Spezialfall, das Single-Source-Shortest-Problem (SSSP), die für SSSP in verteilten Rechenmodellen die erste mit nahe-optimaler Anzahl von Kommunikationsrunden ist. Der zweite Teil handelt von fundamentalen Problemen der Computeralgebra. (1) Wir geben einen Algorithmus zum Berechnen der komplexen Nullstellen eines komplexen Polynoms an, der eine vergleichbare Bitkomplexität zu vorherigen besten Resultaten hat, aber vergleichsweise einfach und daher vielversprechend für die Praxis ist. (2)Wir erweitern den darin verwendeten Pellet-Test zum Zählen der Nullstellen eines Polynoms auf Polynomsysteme, sodass wir die Existenz einer k-fachen Nullstelle eines Systems in einer gegebenen Region zertifizieren können. Für bivariate Systeme zeigen wir experimentell, dass eine Integration dieses Ansatzes in eine Eliminationsmethode zu einer signifikanten Verbesserung führt

    Using MapReduce Streaming for Distributed Life Simulation on the Cloud

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    Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp
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