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检索条件"主题词=APPROXIMATION algorithms"

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approximation algorithms for Fragmenting a Graph Against a Stochastically-Located Threat

Approximation Algorithms for Fragmenting a Graph Against a S...

引用

9th International Workshop on approximation and Online algorithms (WAOA 2011)

作者： Shmoys, David B. Spencer, Gwen Cornell Univ Sch ORIE Ithaca NY 14853 USA Cornell Univ Dept Comp Sci Ithaca NY 14853 USA Dartmouth Coll Neukom Inst Hanover NH 03755 USA

ISBN: (纸本)9783642291159

Motivated by issues in allocating limited preventative resources to protect a landscape against the spread of a wildfire from a stochastic ignition point, we give approximation algorithms for a new family of stochastic optimization problems. We study several models in which we are given a graph with edge costs and node values, a budget, and a probabilistic distribution over ignition nodes: the goal is to find a budget-limited set of edges whose removal protects the largest expected value from being reachable from a stochastic ignition node. In particular, 2-stage stochastic models capture the tradeoffs between preventative treatment and real-time response. The resulting stochastic cut problems are interesting in their own right, and capture a number of related interdiction problems, both in the domain of computational sustainability, and beyond. In trees, even the deterministic problem is (weakly) NP hard: we give a Polynomial-time approximation scheme for the single-stage stochastic case in trees when the number of scenarios is constant. For the 2-stage stochastic model in trees we give a -approximation in trees which violates the budget by a factor of at most 2 (delta is the tree diameter), and a 0.387-approximation that is budget-balanced. For the single-stage stochastic case in trees we can save (1- (1 - 1/delta) (delta)) OPT without violating the budget. Single-stage results extend to general graphs with an additional O(log n) loss in budget-balancedness. Multistage results have a similar extension when the number of scenarios is constant. In an extension of the single-stage model where both ignition and spread are stochastic we give a -approximation in trees. Our approximation guarantees in trees also hold for multistage and probabilistic-element-failure generalizations of the Maximum Coverage with Knapsack Constraint problem (MCKP).

关键词： approximation algorithms Multistage Stochastic Optimization Graphs Containing contagion Sustainability

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approximation algorithms for Computing Maximin Share Allocations 1

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42nd International Colloquium on Automata, Languages and Programming (ICALP)

作者： Amanatidis, Georgios Markakis, Evangelos Nikzad, Afshin Saberi, Amin Athens Univ Econ & Business Dept Informat Athens Greece Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

ISBN: (数字)9783662476727

ISBN: (纸本)9783662476727;9783662476710

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of n agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would be allowed to partition the goods in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then in our problem is to find a partition, so that each agent is guaranteed her maximin share. In settings with indivisible goods, such allocations are not guaranteed to exist, hence, we resort to approximation algorithms. Our main result is a 2/3-approximation, that runs in polynomial time for any number of agents. This improves upon the algorithm of Procaccia and Wang [14], which also produces a 2/3-approximation but runs in polynomial time only for a constant number of agents. We then investigate the intriguing case of 3 agents, for which it is already known that exact maximin share allocations do not always exist. We provide a 6/7-approximation algorithm for this case, improving on the currently known ratio of 3/4. Finally, we undertake a probabilistic analysis. We prove that in randomly generated instances, with high probability there exists a maximin share allocation. This can be seen as a justification of the experimental evidence reported in [5,14], that maximin share allocations exist almost always.

关键词： approximation algorithms

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approximation algorithms in the Successive Hitting Set Model 26th

Approximation Algorithms in the Successive Hitting Set Model

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26th International Symposium on algorithms and Computation (ISAAC)

作者： Storandt, Sabine Univ Freiburg Dept Comp Sci Hugstetter Str 55 D-79106 Freiburg Germany

ISBN: (纸本)9783662489710;9783662489703

We introduce the successive Hitting Set model, where the set system is not given in advance but a set generator produces the sets that contain a specific element from the universe on demand. Despite incomplete knowledge about the set system, we show that several approximation algorithms for the conventional Hitting Set problem can be adopted to perform well in this model. We describe, and experimentally investigate, several scenarios where the new model is beneficial compared to the conventional one.

关键词： approximation algorithms Set (Psychology) Incomplete knowledge Generating sets Universe advance SETTING

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approximation algorithms for Path TSP, ATSP, and TAP viaRelaxations

Approximation Algorithms for Path TSP, ATSP, and TAP viaRela...

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作者： Gao, Zhihan University of Waterloo

学位级别：doctor

Linear programming (LP) relaxations provide a powerfultechnique to design approximation algorithms for combinatorialoptimization problems. In the first part of the thesis, we studythe metric s-t path Traveling Salesman Problem (TSP) via LPrelaxations. We first consider the s-t path graph-TSP, acritical special case of the metric s-t path TSP. We design a newsimple LP-based algorithm for the s-t path graph-TSP that achievesthe best known approximation factor of 1.5. Then, we turn ourattention to the general metric s-t path TSP. [An, Kleinberg, andShmoys, STOC 2012] improved on the long standing 5/3-approximationfactor and presented an algorithm that achieves an approximationfactor of (1+\sqrtapproximation)/2 \approx 1.61803. Later, [Sebo, IPCO 2013]further improved the approximation factor to 8/5. We present asimple, self-contained analysis that unifies both ***, we compare two different LP relaxations of the s-tpath TSP, namely the path version of the Held-Karp LP relaxationfor TSP and a weaker LP relaxation, and we show that both LPs havethe same (fractional) optimal value. Also, we show that the minimumcost of integral solutions of the two LPs are within a factor of3/2 of each other. Furthermore, we prove that a half-integralsolution of the stronger LP relaxation of cost c can be rounded toan integral solution of cost at most 3c/2. Finally, we give aninstance that presents obstructions to two natural methods that aimfor an approximation factor of 3/2. The Sherali-Adams (SA)system and the Lasserre (Las) system are two popularLift-and-Project systems that tighten a given LP relaxation in asystematic way. In the second part of the thesis, we study theAsymmetric Traveling Salesman Problem (ATSP) and unweighted TreeAugmentation Problem, respectively, in the framework of the SAsystem and the Las system. For ATSP, our focus is on negativeresults. For any fixed integer t>=0 and small \epsilon,00 can be any small constant, byanalyzing a combinatorial algorithm. T

关键词： approximation algorithms Path Traveling Salesman Problem Asymmetric Traveling Salesman Problem Tree Augmentation Problem Linear programming relaxations Lift-and-Project systems

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approximation algorithms for the teachers assignment problem 13

Approximation algorithms for the teachers assignment problem

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13th International Symposium on Operational Research, SOR 2015

作者： Cechlárová, Katarína Eirinakis, Pavlos Fleiner, Tamás Magos, Dimitrios Mourtos, Ioannis Ocel'áková, Eva Institute of Mathematics Faculty of Science P.J. Šafárik University Košice Slovakia Department of Management Science and Technology Athens University of Economics and Business 76 Patission Ave. Athens104 34 Greece Budapest University of Technology and Economics MTA-ELTE Egerváry Research Group Budapest Hungary Department of Informatics Technological Educational Institute of Athens Ag. Spyridonos Str. Egaleo12210 Greece

ISBN: (纸本)9789616165457

We study the assignment of trainee teachers to schools for a practical placement. The starting point is the situation characteristic for Slovak and Czech education system where each pre-service teacher specializes in two subjects. It is known that when each school has a certain upper limit for the number of assignees whose specialization involves a given subject, the problem of assigning the maximum number of trainee teachers is NP-hard. In this paper we propose several approximation algorithms for this problem.

关键词： approximation algorithms

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approximation algorithms for reducing the spectral radius to control epidemic spread

Approximation algorithms for reducing the spectral radius to...

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SIAM International Conference on Data Mining 2015, SDM 2015

作者： Saha, Sudip Adiga, Abhijin Prakash, B. Aditya Vullikanti, Anil Kumar S. NDSSL Virginia Bioinformatics Institute Virginia Tech. United States Department of Computer Science Virginia Tech. United States

ISBN: (纸本)9781510811522

The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the 'flu-like' SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motivates a strategy to control epidemic spread by reducing the spectral radius of the underlying network. In this paper, we develop a suite of provable approximation algorithms for reducing the spectral radius by removing the minimum cost set of edges (modeling quarantining) or nodes (modeling vaccinations), with different time and quality tradeoffs. Our main algorithm, GreedyWalk, is based on the idea of hitting closed walks of a given length, and gives an O(log2 rt)-approximation, where n denotes the number of nodes;it also performs much better in practice compared to all prior heuristics proposed for this problem. We further present a novel sparsification method to improve its running time. In addition, we give a new primal-dual based algorithm with an even better approximation guarantee (O(logn)), albeit with slower running time. We also give lower bounds on the worst-case performance of some of the popular heuristics. Finally we demonstrate the applicability of our algorithms and the properties of our solutions via extensive experiments on multiple synthetic and real networks. Copyright © SIAM.

关键词： approximation algorithms

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approximation algorithms for multi-budgeted network design problems 1

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22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015

作者： Stamoulis, Georgios LAMSADE PSL* Research University Université Paris-Dauphine CNRS UMR 7243 France Universitá della svizzera Italiana Lugano Switzerland

ISBN: (数字)9783319252582

ISBN: (纸本)9783319252575

We study the multi-budgeted version of the Survivable Network Design Problem [3] where, besides the usual connectivity requirements between pairs of points, we also need to satisfy a set of linear constraints (the budgets). For this case, we provide a polynomial time (3,3) bi-criteria approximation algorithm for the problem which is based on combinatorial properties of the extreme point solutions of the natural linear relaxation of the problem. © Springer International Publishing Switzerland 2015.

关键词： approximation algorithms

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approximation algorithms for schema-mapping discovery from data examples 9

Approximation algorithms for schema-mapping discovery from d...

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9th Alberto Mendelzon International Workshop on Foundations of Data Management, AMW 2015

作者： Ten Cate, Balder Kolaitis, Phokion G. Qian, Kun Tan, Wang-Chiew University of California Santa Cruz United States Logic Blox Inc. United States IBM Research Almaden United States

In recent years, data examples have been at the core of several different approaches to schema-mapping design. In particular, Gottlob and Senellart introduced a framework for schema-mapping discovery from a single data example, in which the derivation of a schema mapping is cast as an optimization problem. Our goal is to refine and study this framework in more depth. Among other results, we design a polynomial-time log(n)- approximation algorithm for computing optimal schema mappings from a given data example, for a restricted class of schema mappings;moreover, we show that this approximation ratio cannot be improved.

关键词： approximation algorithms

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approximation algorithms for Graph ProtectionProblems

Approximation Algorithms for Graph ProtectionProblems

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作者： Lange, Alexander University of Waterloo

学位级别：master

We study a budgeted cut problem known as GraphProtection, where the goal is to remove edges of a given graph inorder to protect valuable nodes from stochastic, infectiousthreats. This problem was recently proposed by Shmoys and Spencerto model challenges associated with wildfire prevention whenresources are limited and only probabilistic data of ignitionlocation is known. The input consists of a graph with node valuesand edge costs, a budget, and probabilistic data signifying thelikelihood a set of nodes will ignite; the goal is to remove a setof edges with total cost at most the budget so as to maximize theexpected protected value unreachable from these stochasticignition scenarios. Our focus is on the design of approximationalgorithms for Graph Protection when an ignition scenario cancontain an arbitrary number of nodes, a setting mostly left openin the literature. Our main positive result is the design ofconstant-factor approximation algorithms for Graph Protection whenthe input graph is a tree and each node has an independent chanceof being an ignition point. We also show that in the general casewhen ignition probabilities are defined by a distribution oversubsets of nodes, the problem becomes at least as hard as theDensest k-Subgraph problem and thus, such an approximationalgorithm is unlikely to exist

关键词： approximation algorithms graph protection

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Exact and approximation algorithms for Weighted Matroid Intersection 16

Exact and Approximation Algorithms for Weighted Matroid Inte...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Chien-Chung Huang Naonori Kakimura Naoyuki Kamiyama Department of Computer Science and Engineering Chalmers University of Technology Graduate School of Arts and Sciences University of Tokyo Institute of Mathematics for Industry Kyushu University

ISBN: (纸本)9781510819672

In this paper, we propose new exact and approximation algorithms for the weighted matroid intersection problem. Our exact algorithm is faster than previous algorithms when the largest weight is relatively small. Our approximation algorithm delivers a (1 - ε)-approximate solution with a running time significantly faster than known exact algorithms. The core of our algorithms is a decomposition technique: we decompose an instance of the weighted matroid intersection problem into a set of instances of the unweighted matroid intersection problem. The computational advantage of this approach is that we can make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms. Precisely speaking, we prove that we can solve the weighted matroid intersection problem via solving W instances of the unweighted matroid intersection problem, where W is the largest given weight. Furthermore, we can find a (1 - ε)-approximate solution via solving O(ε~(-1) log r) instances of the unweighted matroid intersection problem, where r is the smallest rank of the given two matroids. Our algorithms are simple and flexible: they can be adapted to special cases of the weighted matroid intersection problem, using specialized unweighted matroid intersection algorithms. In this paper, we will show the following results. 1. Given two general matroids, using Cunningham's algorithm, we can solve the weighted matroid intersection problem exactly in O(τε~(-1)nr~(1.5)) time and (1 - ε)-approximately in O(τε~(-1)nr~(1.5) log r) time, where n is the size of the ground set and τ is the time complexity of an independence oracle call. 2. Given two graphic matroids, using the algorithm of Gabow and Xu, we can solve the weighted matroid intersection problem exactly in O(W{the square root of} log) r) time and (1 - ε)-approximately in O(ε~(-1) {the square root of} log~2 r) time. 3. Given two linear matroids (in the form of two r-by-n matrices), using the algorithm of Cheung, Kwok,

关键词： Matroid approximation algorithms Intersection algorithms Crossing Exact complexity classes limit dimensions

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