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检索条件"丛书名=Proceedings in Applied Mathematics"

共 197 条记录，以下是71-80 订阅

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Inapproximability for planar embedding problems

Inapproximability for planar embedding problems

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Edmonds, Jeff Sidiropoulos, Anastasios Zouzias, Anastasios York Univ N York ON M3J 1P3 Canada

ISBN: (纸本)9780898717013

We consider the problem of computing a minimum-distortion bijection between two point-sets in R-2 We prove the first non-trivial inapproximability result lot this problem I'm the case when the distortion is constant More precisely. we show that, there exist constants 0 < alpha < beta, such that it, is NP-hard to distinguish between spaces for which the distortion is either at most alpha, or at least, beta, under the Euclidean norm This addresses a question of Kenyon. Rabani and Sinclair [KRS04], and extends a result, due to Papadimitriou and Safra [PS05], who gave inapproximability for point-sets in R-3 We also apply similar ideas to the problem of computing a minimum-distortion embedding of a finite metric space into R-2 We obtain an analogous inapproximability result under the l(infinity) noun for this problem Inapproximability tot the case of constant distortion was previously known only for dimension at, least 3 [MS08]

关键词： Geometry

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Fully-Functional Succinct Trees

Fully-Functional Succinct Trees

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Sadakane, Kunihiko Navarro, Gonzalo Res Org Informat & Syst Natl Inst Informat Chiyoda Ku 2-1-2 Hitotsubashi Tokyo 1018430 Japan

ISBN: (纸本)9780898717013

We propose new succinct representations of ordinal trees, winch have been studied extensively. It is known that any n-node static tree can be represented in 2n + o(n) bits and a large number of operations on the tree can be supported in constant time under the word-RAM model. However existing data structures are not satisfactory in both theory and practice because (1) the lower-order term is Omega(n log log n/ log n), which cannot be neglected in practice, (2) the hidden constant is also large, (3) the data structures arc complicated and difficult to implement, and (4) the techniques do not extend to dynamic trees supporting insertions and deletions of nodes We propose a simple and flexible data structure, called the mange min-max Lice, that reduces the large number of relevant tree operations considered in the literature to a few primitives, which are carried out in constant tune on sufficiently small trees The result is then extended to trees of arbitrary size, achieving 2n + O(n/polylog(n)) bits of space The redundancy is significantly lower than in any previous proposal, and the data structure is easily implemented Furthermore, using the same framework, we derive the first fully-functional dynamic succinct, trees

关键词： Data structures

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SRPT is 1.86-Competitive for Completion Time Scheduling

SRPT is 1.86-Competitive for Completion Time Scheduling

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chung, Christine Nonner, Tim Souza, Alexander Univ Pittsburgh Dept Comp Sci Pittsburgh PA 15260 USA Univ Freiburg Dept Comp Sci Freiburg Germany Humboldt Univ Dept Comp Sci Berlin Germany

ISBN: (纸本)9780898717013

We consider the classical problem of scheduling preemptible jobs, that arrive over time, on identical parallel machines The goal is to minimize the total completion time of the jobs. In standard scheduling notation of Graham et al [5], this problem is denoted P vertical bar r(j), pmtn vertical bar Sigma(j) c(j.) A popular algorithm called SRPT, which always schedules the unfinished jobs with shortest remaining processing time, is known to be 2-competitive, see Phillips et al [13, 14]. This is also the best known competitive ratio for any online algorithm However, it is conjectured that the competitive ratio of SRPT. is significantly less than 2 Even breaking the barrier of 2 is considered a significant step towards the final answer of this classical online problem. We improve on this open problem by showing that SRPT is 1.86-competitive. This result is obtained using the following method, which might be of general interest: We define two dependent random variables that sum up to the difference between the cost of an SRPT schedule and the cost of an optimal schedule. Then we bound the sum of the expected values of these random variables with respect to the cost of the optimal schedule, yielding the claimed competitiveness. Furthermore, we show a lower bound of 21/19 for SRPT, improving on the previously best known 12/11 due to Lu et al. [11].

关键词： Costs

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Belief Propagation for Min-cost Network Flow: Convergence & Correctness

Belief Propagation for Min-cost Network Flow: Convergence & ...

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gamarnik, David Shah, Devavrat Wei, Yehua MIT Ctr Operat Res Sch Management Cambridge MA 02139 USA MIT EECS Cambridge MA 02139 USA MIT Ctr Operat Res Cambridge MA 02139 USA

ISBN: (纸本)9780898717013

We formulate a Belief Propagation (BP) algorithm in the context of the capacitated in network flow problem (MCF) Unlike most of the instances of BP studied in the past, the messages of BP in the context of this problem are piecewise-linear functions We wove that BP converges to the optimal solution in pseudo-polynomial time, provided that the optimal solution is unique and the problem input is integral Moreover, we present a simple modification of the BP algorithm which gives a fully polynomial-time randomized approximation scheme (FPRAS) for MCF This is the first instance where BP is proved to have fully-polynomial running time.

关键词： Belief propagation

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Shape Replication through Self-Assembly and RNase Enzymes

Shape Replication through Self-Assembly and RNase Enzymes

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Abel, Zachary Benbernou, Nadia Damian, Mirela Demaine, Erik D. Demaine, Martin L. Flatland, Robin Kominers, Scott D. Schweller, Robert Harvard Univ Dept Math Cambridge MA 02138 USA MIT comp sci & artificial Intelligence Lab Cambridge MA 02139 USA Villanova Univ Dept Comp Sci Villanova PA 19085 USA Siena Coll Dept Comp Sci Giza 12211 Egypt Univ Texas-Pan Amer Dept Comp Sci Edinburg TX 78539 USA

ISBN: (纸本)9780898717013

We introduce the problem of shape replication in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model in which tiles consisting of DNA or RNA can be dynamically added in a sequence of stages. We further permit the addition of RNase enzymes capable of disintegrating RNA tiles. Under this model, we show that arbitrary genus-0 shapes can be replicated infinitely many times using only O(1) distinct tile types and O(1) stages. Further, we show how to replicate precisely n copies of a shape using O(log n) stages and O(1) tile types.

关键词： Self assembly

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Faster exponential time algorithms for the shortest vector problem

Faster exponential time algorithms for the shortest vector p...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Micciancio, Daniele Voulgaris, Panagiotis Univ Calif San Diego La Jolla CA 92093 USA

ISBN: (纸本)9780898717013

We present new faster algorithms for the exact solution of the shortest;vector problem in arbitrary lattices Our main result shows that the shortest vector in any n-dimensional lattice can be found in time 2(3) (199n) (and space 2(1) (325n)), or in Space 2(1) (095n) (and still tune 2(O(n))). Tins improves the best previously known algorithm by Ajtai, Kumar and Sivakumar [proceedings of STOC 2001] which was shown by Nguyen and Vidick [J Math Crypto. 2(2) 181-207] to inn in time 2(5) (9n) and space 2(2) (95n) We also present a practical variant of our algorithm which provably uses an amount of space proportional to tau(n), the "kissing" constant in dimension n. No upper bound on the running tune of our second algorithm is currently known, but experimentally the algorithm seems 1,0 perforin fairly well in practice with running Lime 2(0) (52n) and space complexity 2(0) (2n)

关键词： Algorithm Analysis Cryptography Shortest Vector Problem Sieving algorithms Software implementations

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Maximum Flows and Parametric Shortest Paths in Planar Graphs

Maximum Flows and Parametric Shortest Paths in Planar Graphs

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Erickson, Jeff Univ Illinois Dept Comp Sci Urbana IL 61801 USA

ISBN: (纸本)9780898717013

We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G* This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once The resulting maximum-flow algorithm is identical to the recent algorithm of Borradaile and Klein [J ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change Omega(n(2)) times in the worst case, suggesting that a different method may be required to efficiently compute maximum flows in higher-genus graphs.

关键词： Forestry

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A Constant Factor Approximation Algorithm for Generalized Min-Sum Set Cover

A Constant Factor Approximation Algorithm for Generalized Mi...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Bansal, Nikhil Gupta, Anupam Krishnaswamy, Ravishankar IBM Corp TJ Watson Res Ctr Yorktown Hts NY 10598 USA Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA

ISBN: (纸本)9780898717013

Consider the following generalized mm-sum set cover or multiple intents re-ranking problem proposed by Azar et al. (STOC 2009). We are given a universe of elements and a collection of subsets, with each set S having a covering requirement of K(S). The objective is to pick one element at a time such that the average covering time of the sets is minimized, where the covering time of a set S is the first time at which K (S) elements from it have been selected. There are two well-studied extreme cases of this problem. (i) when K (S) = 1 for all sets, we get the min-sum set cover problem, and (ii) when K (S) = 181 for all sets, we get the minimum-latency set cover problem. Constant factor approximations are known for both these problems. In their paper, Azar et al. considered the general problem and gave a logarithmic approximation algorithm for it. In this paper, we improve then result and give a simple randomized constant factor approximation algorithm for the generalized min-sum set cover problem.

关键词： Approximation algorithms

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Phase Transition for the Mixing Time of the Glauber Dynamics for Coloring Regular Trees

Phase Transition for the Mixing Time of the Glauber Dynamics...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Tetah, Prasad Vera, Juan C. Vigoda, Eric Yang, Linji Georgia Inst Technol Sch Math Atlanta GA 30332 USA Tilburg Univ Dept Econometr & Operat Res NL-5000 LE Tilburg Netherlands Georgia Inst Technol Sch Comp Sci Atlanta GA 30332 USA

ISBN: (纸本)9780898717013

We prove that the in time of the Glauber dynamics or random k-colorings of the complete Lice with blanching factor b undergoes a phase transition at k = b(1 + o(b)(1))/In b Our main result shows nearly sharp bounds on the mixing tune of the dynamics on the complete tree with n vertices for k = Cb/In b colors with constant C For C >= 1 we prove the mixing time is O(n(1+ob(1)) In-2 n) On the other side, for C < 1 the mixing time experiences a slowing down, in particular. we prove it is O(n(1/C + ob(1)) In-2 n) and Omega(n(1/C - ob(1))) The critical point C = 1 is interesting since it coincides (at least up to first older) to the so-called reconstruction threshold which was recently established by Sly The reconstruction threshold has been of considerable interest recently since It appeals to have close connections to the efficiency of certain local algorithms, and this work was inspired by our attempt to understand these connections in this particular setting.

关键词： Mixing

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Fast SDP Algorithms for Constraint Satisfaction Problems

Fast SDP Algorithms for Constraint Satisfaction Problems

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Steurer, David Princeton Univ Dept Comp Sci Princeton NJ 08544 USA

ISBN: (纸本)9780898717013

The class of constraint satisfactions problems (CSPs) captures many fundamental combinatorial optimization problems such as MAX CUT, MAX q-CUT, UNIQUE GAMES, and MAX l-SAT Recently, Raghavendra (STOC'OS) identified a simple semidefinite programming relaxation that gives the best possible approximation for any CSP, assuming the Unique Games Conjecture Raghavendra and Steurer (FOCS'09) showed that, independent of the truth of the Unique Games Conjecture the integrality gap of this relaxation cannot be improved even by adding a large class of valid inequalities. We present an algorithm that finds an approximately optimal solution to this relaxation in near-linear time. Combining this algorithm with a rounding scheme of Raghavendra and Steurer (FOCS'09) leads to an approximation algorithm for any CSP that runs in near-linear tune and has an approximation guratantee that matches the integrality gap;which is optimal assuming the Unique Gaines Conjecture

关键词： Constraint satisfaction problems

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