10,468 research outputs found

    Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

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    The generalized minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph for which the vertices are divided into clusters. Such spanning tree includes only one vertex from each cluster. Despite the diverse practical applications for this problem, the NP-hardness continues to be a computational challenge. Good quality solutions for some instances of the problem have been found by combining specific heuristics or by including them within a metaheuristic. However studied combinations correspond to a subset of all possible combinations. In this study a technique based on a genotype-phenotype genetic algorithm to automatically construct new algorithms for the problem, which contain combinations of heuristics, is presented. The produced algorithms are competitive in terms of the quality of the solution obtained. This emerges from the comparison of the performance with problem-specific heuristics and with metaheuristic approaches

    Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

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    Bicriteria Network Design Problems

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    We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

    A nearly-mlogn time solver for SDD linear systems

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    We present an improved algorithm for solving symmetrically diagonally dominant linear systems. On input of an n×nn\times n symmetric diagonally dominant matrix AA with mm non-zero entries and a vector bb such that Axˉ=bA\bar{x} = b for some (unknown) vector xˉ\bar{x}, our algorithm computes a vector xx such that xxˉA<ϵxˉA||{x}-\bar{x}||_A < \epsilon ||\bar{x}||_A {A||\cdot||_A denotes the A-norm} in time O~(mlognlog(1/ϵ)).{\tilde O}(m\log n \log (1/\epsilon)). The solver utilizes in a standard way a `preconditioning' chain of progressively sparser graphs. To claim the faster running time we make a two-fold improvement in the algorithm for constructing the chain. The new chain exploits previously unknown properties of the graph sparsification algorithm given in [Koutis,Miller,Peng, FOCS 2010], allowing for stronger preconditioning properties. We also present an algorithm of independent interest that constructs nearly-tight low-stretch spanning trees in time O~(mlogn)\tilde{O}(m\log{n}), a factor of O(logn)O(\log{n}) faster than the algorithm in [Abraham,Bartal,Neiman, FOCS 2008]. This speedup directly reflects on the construction time of the preconditioning chain.Comment: to appear in FOCS1

    Survey of Distributed Decision

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    We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CONGEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model)

    Learning Generalized Reactive Policies using Deep Neural Networks

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    We present a new approach to learning for planning, where knowledge acquired while solving a given set of planning problems is used to plan faster in related, but new problem instances. We show that a deep neural network can be used to learn and represent a \emph{generalized reactive policy} (GRP) that maps a problem instance and a state to an action, and that the learned GRPs efficiently solve large classes of challenging problem instances. In contrast to prior efforts in this direction, our approach significantly reduces the dependence of learning on handcrafted domain knowledge or feature selection. Instead, the GRP is trained from scratch using a set of successful execution traces. We show that our approach can also be used to automatically learn a heuristic function that can be used in directed search algorithms. We evaluate our approach using an extensive suite of experiments on two challenging planning problem domains and show that our approach facilitates learning complex decision making policies and powerful heuristic functions with minimal human input. Videos of our results are available at goo.gl/Hpy4e3
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