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

共 197 条记录，以下是111-120 订阅

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Universal ε-approximators for integrals

Universal ε-approximators for integrals

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Langberg, Michael Schulman, Leonard J. Open Univ Israel Div Comp Sci 108 Ravutski St IL-43107 Raanana Israel CALTECH Pasadena CA 91125 USA

ISBN: (纸本)9780898717013

Let X be a space and F a family of 0, 1-valued functions on X Vapnik and Chervonenkis showed that, if F is "simple" (finite VC dimension), then for every probability measure it on X and epsilon > 0 ther is a finite set S such that for all f is an element of F Sigma(x is an element of S) integral (x)/vertical bar S vertical bar = [integral f(x)d mu(x)] +/- epsilon Think of S as a "universal epsilon-approximator" for intogiation in F S can actually be obtained w h.p. just by sampling a few points from mu This is a mainstay of computational learning theoi y It was later extended by other authors to families of bounded (e.g [0, 1]-valued) real functionsIn this work we establish similar "universal epsilon-approximators" for families of unbounded nonnegative real functions in particular, for the families over winch one optimizes when performing data classification (In tins case the epsilon-apploximation should be multiplicative) Specifically, let be the family of "k-median functions" (or k-means, etc) on R-d with an arbitraly norm Q That is, any set u(1),.,u(k) is an element of R-d determines an f by f(x) = (min(2) Q(x - u(2)))(alpha) (Here alpha >= 0.) Then for every measure mu on R-d and a *** is an element of s f (x) v (x) is an element of (1 +/- epsilon) (integral integral (x) d mu(x)).

关键词： Computation theory

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How good is the Chord algorithm?

How good is the Chord algorithm?

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Daskalakis, Constantinos Diakonikolas, Ilias Yannakakis, Mihalis MIT CSAIL Cambridge MA 02139 USA Univ Edinburgh Sch Informat Edinburgh Scotland Columbia Univ Dept Comp Sci New York NY 10027 USA

ISBN: (纸本)9780898717013

The Chord algorithm is a popular, simple method for the succinct approximation or curves, which is widely used, under different names. in a variety of areas, such as, multi-objective and parametric optimization, computational geometry, and graphics. We analyze the performance of the chord algorithm, as compared to the optimal approximation that achieves a desired accuracy with the minimum number of points. We prove sharp upper and lower bounds, both in the worst case and average case setting

关键词： Computational geometry

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On Linear and Semidefinite Programming Relaxations for Hypergraph Matching

On Linear and Semidefinite Programming Relaxations for Hyper...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chan, Yuk Hei Lau, Lap Chi Chinese Univ Hong Kong Dept Comp Sci & Engn Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9780898717013

The hypergraph matching problem is to find a largest;collection of disjoint hyperedges in a hypergraph This IS a well-studied problem in combinatorial optimization and graph theory with various applications The best known approximation algorithms for tins problem ate all local search algorithms hi this paper we analyze different, lineal and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method Our Main results are the following

关键词： Approximation algorithms

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Resource Minimization for Fire Containment

Resource Minimization for Fire Containment

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chalermsook, Parinya Chuzhoy, Julia Univ Chicago Dept Comp Sci Chicago IL 60637 USA Toyota Technol Inst Chicago IL 60637 USA

ISBN: (纸本)9780898717013

We consider the following model for fire containment We ale given an undirected graph G = (V, E) with a source vertex s where the lire stalls At each time step, the firefighters can save up to k vertices of the graph, while the fire spreads from burning vertices to all then neighbors that have not been saved so fat Out goal is to choose the vertices to be saved at each time step so as to contain the fire This is a. simple mathematical model abstracting the dynamic nature of lire containment and other natural processes, such as. for example, the spread of a. perfectly contagious disease and its containment via vaccination

关键词： Fires

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An O(log n/log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem

An O(log n/log log n)-approximation Alg...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Asadpour, Arash Goemans, Michel X. Madry, Aleksander Gharan, Shayan Oveis Saberi, Amin Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA MIT Dept Math Cambridge MA 02139 USA MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

We consider the Asymmetric Traveling Salesman problem for costs satisfying the triangle inequality. We derive a randomized algorithm which delivers a solution within a factor O(log n/ log log n) of the optimum with hi... 详细信息

ISBN: (纸本)9780898717013

关键词： Approximation algorithms

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Quasirandom Load Balancing

Quasirandom Load Balancing

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Friedrich, Tobias Gairing, Martin Sauerwald, Thomas Max Planck Inst Informat Saarbrucken Germany Univ Liverpool Liverpool L69 3BX Merseyside England Simon Fraser Univ Burnaby BC Canada

ISBN: (纸本)9780898717013

We propose a simple distributed algorithm km balancing indivisible tokens On graphs The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm approximates the idealized process (where the tokens are divisible) on important network topologies surprisingly closely On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant In contrast to that, the randomized rounding approach of Friedrich and Sauerwald [8] can deviate up to Omega(poly log n) and the deterministic algorithm of Rabani, Sinclair and Wanka. [23] has a deviation of Omega(n(1/d)) This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness We further show that also on the hypercube our algorithm has a. smaller deviation from the idealized process than the previous algorithms To prove these results, we derive several combinatorial and probabilistic results that we believe to be of independent interest In particular, we show that first-passage probabilities of a. random walk on a path with arbitrary weights can be expressed as a convolution of independent, geometric probability distributions.

关键词： Probability distributions

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PTAS for maximum weight independent set problem with random weights in bounded degree graphs

PTAS for maximum weight independent set problem with random ...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gamarnik, David Goldberg, David Weber, Theophane MIT Ctr Operat Res Cambridge MA 02139 USA

ISBN: (纸本)9780898717013

Finding the largest independent set in a graph is a notoriously difficult, NP-complete combinatorial optimization problem. Moreover, even for graphs with largest degree 3, no polynomial time approximation algorithm exists with a 1.0071-factor approximation guarantee, unless P = NP [BK98]. We consider the related problem of finding the maximum weight independent set in a bounded degree graph;when the node weights are generated lid from a common distribution. Surprisingly;we discover that the problem becomes tractable for certain distributions Specifically, we construct a randomized PTAS (Polynomial-Tune Approximation Scheme) for the case of exponentially distributed weights and arbitrary graphs with degree at most 3. We extend our result to graphs with larger constant degrees but for distributions which are mixtures of exponential distributions. At the same time, we prove that no PTAS exists for computing the expected size of the maximum weight independent set in the case of exponentially distributed weights for graphs with sufficiently large constant degree, unless P=NP Our algorithm, cavity expansion, is new and is based on the combination of several powerful ideas, including recent deterministic approximation algorithms for counting on graphs and local weak convergence/correlation decay methods

关键词： Approximation algorithms

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A Nearly Optimal Algorithm for Approximating Replacement Paths and k Shortest Simple Paths in General Graphs

A Nearly Optimal Algorithm for Approximating Replacement Pat...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Bernstein, Aaron MIT Cambridge MA 02139 USA

ISBN: (纸本)9780898717013

Let G = (V, E) be a directed graph with positive edge weights, let s, t be two specified vertices in this graph, and let pi(s, t) be the shortest path between them In the replacement paths problem we want to compute, for every edge e on pi(s, 1), the shortest path from s to t that avoids e. The naive solution to this problem would be to remove each edge e, one at a time, and compute the shortest s - t path each time, this yields a running time of O(mn, + n(2) log n). Gotthilf and Lewenstein [8] recently improved this to O(mn +n(2) log log n), but no o(mn) algorithms are known. We present. the first, approximation algorithm for replacement, paths in directed graphs with positive edge weights Given any epsilon is an element of [0, 1) our algorithm returns (1 + epsilon)-approximate replacement paths in O(epsilon(-1) log(2) n log(nC/c)(m+n log n)) = (O) over tilde (m log(nC/c)/epsilon) time, where C is the largest edge weight in the graph and c is the smallest, weight We also present. an even faster (1 + epsilon) approximate algorithm for the simpler problem of approximating the k shot test simple s - t paths in a directed graph with positive edge weights. That is: out algorithm outputs k different simple s - t paths, where the kill path we output is a (1 + epsilon) approximation to the actual kth shortest simple s - t path The running time of our algorithm is O(k epsilon(-1) log(2) n(m + n log n)) = (O) over tilde (km/epsilon) The fastest exact algorithm for this problem has a running time of O(k(mn + n(2) log log n)) = (O) over tilde (kmn) [8] The previous best approximation algorithm was developed by Roditty [15];it has a stretch of 3/2 and a running time of (O) over tilde (km root n) (it, does not work for replacement paths) Note that;all of our running times are nearly optimal except for the O(log(nC/c)) factor in the replacements paths algorithm Also, our algorithm can solve the variant of approximate replacement paths where we avoid vertices instead of edges

关键词： Directed graphs

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An Online Scalable Algorithm for Average Flow Time in Broadcast Scheduling

An Online Scalable Algorithm for Average Flow Time in Broadc...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Im, Sungjin Moseley, Benjamin Univ Illinois Dept Comp Sci 201 N Goodwin Ave Urbana IL 61801 USA

ISBN: (纸本)9780898717013

In this paper the online pull-based broadcast model is considered In this model;there are n pages of data stored at a set vet and requests arrive lot pages online When the server broadcasts page p;all outstanding requests for the same page p arc simultaneously satisfied We consider the ploblem of minimizing average (total) flow time online where all pages ale unit-sized For this problem, there has been a decade-long search for an on algorithm which is scalable, (1 + epsilon)-speed O(1)-competitive for any fixed epsilon > 0. In this paper, we give the first analysis of an online scalable algorithm

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On the Equilibria of Alternating Move Games

On the Equilibria of Alternating Move Games

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Roth, Aaron Balcan, Maria Florina Kalai, Adam Mansour, Yishay Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA Georgia Inst Technol Atlanta GA 30332 USA Microsoft Res Redmond WA 98052 USA Geogle Res & Tel Aviv Univ IL-69978 Tel Aviv Israel

ISBN: (纸本)9780898717013

We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an epsilon-approximate equilibrium of an alternating move game with any number of players. In contrast, it is known that for k >= 3 players, there is no FPTAS for computing Nash equilibria of simultaneous move repeated games unless P = PPAD. We also consider equilibria in memoryless strategies, which are guaranteed to exist in two player games. We show that for the special case of k = 2 players, all but a negligible fraction of games admit an equilibrium in pure memoryless strategies that can be found in polynomial time. Moreover, we give a PTAS to compute an epsilon- approximate equilibrium in pure memoryless strategies in any 2 player game that admits an exact equilibrium in pure memoryless strategies.

关键词： Game theory

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