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

共 197 条记录，以下是101-110 订阅

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Sharp Dichotomies for Regret Minimization in Metric Spaces

Sharp Dichotomies for Regret Minimization in Metric Spaces

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Kleinberg, Robert Slivkins, Aleksandrs Cornell Univ Dept Comp Sci Ithaca NY 14853 USA Microsoft Res Mountain View CA 94043 USA

ISBN: (纸本)9780898717013

The Lipschitz multi-armed bandit (MAB) problem generalizes the classical multi-armed bandit problem by assuming one is given side information consisting of a priori upper bounds on the difference in expected payoff between certain pairs of strategies. Classical results of Lai-Robbins [28] and Auer et al. [3] imply a logarithmic regret bound for the Lipschitz MAB problem on finite metric spaces. Recent results on continuum-armed bandit problems and their generalizations imply lower bounds of root t, or stronger, for many infinite metric spaces such as the unit interval. Is this dichotomy universal? We prove that the answer is yes: for every metric space, the optimal regret of a Lipschitz MAB algorithm is either bounded above by any f is an element of omega(log t), or bounded below by any g is an element of o(root t). Perhaps surprisingly, this dichotomy does not coincide with the distinction between finite and infinite metric spaces;instead it depends on whether the completion of the metric space is compact and countable. Our proof connects upper and lower bound techniques in online learning with classical topological notions such as perfect sets and the Cantor-Bendixson theorem. We also consider the full-feedback (a.k.a., best-expert) version of Lipschitz MAB problem, termed the Lipschitz experts problem, and show that this problem exhibits a similar dichotomy. We proceed to give nearly matching upper and lower bounds on regret in the Lipschitz experts problem on uncountable metric spaces. These bounds are of the form (Theta) over tilde (t(r)), where the exponent gamma is an element of [1/2,1] depends on the metric space To characterize this dependence, we introduce a novel dimensionality notion tailored to the experts problem. Finally, we show that both Lipschitz bandits and Lipschitz experts problems become completely intractable (in the sense that no algorithm has regret o(t)) if and only if the completion of the metric space is non-compact.

关键词： Topology

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1-Pass Relative-Error L_p-Sampling with Applications

1-Pass Relative-Error Lp-Sampling with App...

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Monemizadeh, Morteza Woodruff, David P. Univ Dortmund Dept Comp Sci D-44221 Dortmund Germany

ISBN: (纸本)9780898717013

For any p is an element of [0,2] we give a 1-pass poly(epsilon(-1) log n)-space algorithm which, given a data stream of length an with insertions and deletions of an n-dimensional vector a, with updates in the range {-M, -M + 1, ... , M -1, M}, outputs a sample of [n] = {1,2, n} for which for all a the probability that a is returned is (1 c)-LELL- n(-C), where at denotes the (possibly negative) value of coordinate i, F-p (a) = Sigma(n)(i=1)vertical bar a(i)vertical bar(p) = parallel to a parallel to(p)(p) denotes the p-th frequency moment, (le, the p-th power of the L-p norm), and C > 0 is an arbitrarily huge constant,. Here we assume that a, in, and M are polynomially related Our generic sampling framework improves and unifies algorithms for several communication and streaming problems, including cascaded norms, heavy hitters, and moment estimation. It also gives the first relative-error forward sampling algorithm in a data stream with deletions, answering an open question of Col mode et al.

关键词： Vector spaces

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A 1.43-Competitive Online Graph Edge Coloring Algorithm In The Random Order Arrival Model

A 1.43-Competitive Online Graph Edge Coloring Algorithm In T...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Bahmani, Bahman Mehta, Aranyak Motwani, Rajeev Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9780898717013

A classic theorem by Vizing proves that if the maximum degree of a graph is Delta, then It is possible to color its edges;in polynomial time;using at most Delta+1 colors However, this algorithm is offline, i e., it assumes the whole graph is known in advance. A natural question then is how well we can do in the online setting, where the edges of the graph are revealed one by one, and we need to color each edge as soon as it is added to the graph. Online edge coloring has an important application in fast switch scheduling. Here, a natural model is that edges arrive online, but in a random permutation Even in the random permutations model, the best analysis for any algorithm is factor 2, which comes from the simple greedy algorithm (which is factor 2 even in the worst case online model). The algorithm of Aggarwal et al. [1] provides a 1+o(1) factor algorithm, but for the case of multigraphs, when Delta = omega(n(2)), where It is the number of vertices. In this paper, we show that for graphs with Delta = omega(log n), it is possible to color the graph with 1.43 Delta + o(Delta) colors in the online random order model. Our algorithm is inspired by a 1.6 factor distributed offline algorithm of Panconesi and Srinivasan [9], which we extend by reusing colors online in multiple rounds.

关键词： Color

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Differentially Private Combinatorial Optimization

Differentially Private Combinatorial Optimization

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gupta, Anupam Ligett, Katrina McSherry, Frank Roth, Aaron Talwar, Kunal

ISBN: (纸本)9780898717013

Consider the following problem: given a metric space, sonic of whose points are "clients," select a set of at most;k facility locations to minimize the average distance from the clients to their nearest facility This is just the well-studied k-median problem, for which many appioximation algorithms and hardness results are known Note that the objective function encourages opening facilities in areas where there are many clients, and given a solution, it is often possible to get a good idea of where the clients are located This raises the following quandary what if the locations of the clients are sensitive information that we would like to keep private? Is it even possible to design good algorithms for this problem that preserve the privacy of the clients?

关键词： Approximation algorithms

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Randomized Shellsort: A Simple Oblivious Sorting Algorithm

Randomized Shellsort: A Simple Oblivious Sorting Algorithm

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Goodrich, Michael T. Univ Calif Irvine Dept Comp Sci Irvine CA 92717 USA

ISBN: (纸本)9780898717013

In this paper, we describe a randomized Shellsort algorithm This algorithm is a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and succeeds in sorting any given input permutation with very high probability. Taken together, these properties imply applications in the design of new efficient privacy-preserving computations based on the secure multi-party computation (SMC) paradigm In addition, by a trivial conversion of this Monte Carlo algorithm to its Las Vegas equivalent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability.

关键词： Sorting

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Vertices of Degree k in Random Maps

Vertices of Degree k in Random Maps

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Johannsen, Daniel Panagiotou, Konstantinos Max Planck Inst Informat Saarbrucken Germany

ISBN: (纸本)9780898717013

This work is devoted to the study of the typical structure of a random map Maps are planar graphs embedded in the plane We investigate the degree sequences of random maps from families of a certain type, which, among others, includes fundamental map classes like those of biconnected maps, 3-connected maps, and triangulations. In particular;we develop a general framework that allows us to derive relations and exact asymptotic expressions for the expected number of vertices of degree k in random maps from these classes, and also provide accompanying large deviation statements Extending the work of Gao and Wormald (Combinatorica, 2003) on random general maps;we obtain as results of our framework precise information about the number of vertices of degree k in random biconnected, 3-connected, loopless, and bridgeless maps.

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Correlation Clustering with Noisy Input

Correlation Clustering with Noisy Input

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Mathieu, Claire Schudy, Warren Brown Univ Dept Comp Sci Providence RI 02912 USA

ISBN: (纸本)9780898717013

Correlation clustering is a type of clustering that uses a. basic form of input data For every pair of data items, the input specifies whether they ale similar (belonging to the same cluster) or dissimilar (belonging to different clusters) This lamination may be inconsistent, and the goal is to find a clustering (partition of the vertices) that. disagrees with as few pieces of information as possible Colleration clustering is APX-hard for worst-case inputs We study the following semi-random noisy model to generate the input stall, from an arbitrary partition of the vertices into clusters. Then;for each pair of vertices, the similarity information is corrupted (noisy) independently with probability p Finally, an adversary generates the Input by choosing similality/dissimilarity information arbitrarily for each corrupted pair of vertices In this model, out algorithm produces a. clustering with cost at most 1 + O(n(-1/6)) tones the cost of the optimal clustering, as long as p <= 1/2 71- n(-1/3) Moreover, if all clusters have size at least(1) c(1)root n then we can exactly reconstruct the planted clustering If the noise p is small, that p <= n(-delta)/60, then we can exactly reconstruct all clusters of the planted clustering that have size at least 3150/delta, and provide a certificate (witness) proving that those clusters file in any optimal clustering Among other techniques, we use the natural semi-definite programming relaxation followed by an ink-nesting rounding phase The analysis uses SDP duality and spectral properties of random mattices.

关键词： Clustering algorithms

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On Nonlinear Forbidden 0-1 Matrices: A Refutation of a Furedi-Hajnal Conjecture

On Nonlinear Forbidden 0-1 Matrices: A Refutation of a Fured...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Pettie, Seth Univ Michigan Ann Arbor MI 48109 USA

ISBN: (纸本)9780898717013

A 0-1 matrix A is said to avoid a forbidden 0-1 matrix (or pattern) P if no submatrix of A matches P, where a 0 in P matches either 0 or 1 in A. The theory of forbidden matrices subsumes many extremal problems in combinatorics and graph theory such as bounding the length of Davenport-Schinzel sequences and their generalizations, Stanley and Wilf's permutation avoidance problem, and Turan-type subgraph avoidance problems. In addition, forbidden matrix theory has proved to be a powerful tool in discrete geometry and the analysis of both geometric and non-geometric algorithms. Clearly a 0-1 matrix can be interpreted as the incidence matrix of a bipartite graph in which vertices on each side of the partition are ordered. Our primary contribution is a refutation of a conjecture of Furedi and Hajnal: that if P corresponds to an acyclic graph then the maximum number of is in an n x n matrix avoiding P is O(n log n). In addition, we give a simpler proof that there are infinitely many minimal nonlinear patterns and give tight bounds on the extremal functions for several small forbidden patterns.

关键词： Graph theory

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How far can you reach?

How far can you reach?

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Borcea, Ciprian Streinu, Ileana Rider Univ Dept Math Lawrenceville NJ 08648 USA Smith Coll Dept Comp Sci Northampton MA 01063 USA

ISBN: (纸本)9780898717013

The problem of computing the maximum reach configurations of a 31) revolute-jointed manipulator is a long-standing open problem in robotics. In this paper we present an optimal algorithmic solution for orthogonal polygonal chains This appears as a. special case of a larger family, fully characterized here by a technical condition. Until now, in spite of the practical importance of the problem, only numerical optimization heuristics were available, with no guarantee of obtaining the global maximum In fact., the problem was not even known to be computationally solvable, and in practice, the numerical heuristics were applicable only to small problem sizes We present elementary and efficient (mostly linear) algorithms for four fundamental problems. (1) finding the maximum reach value, (2) finding a maximum reach configuration (or enumerating all of them), (3) folding a given chain to A given maximum position, and (4) folding a chain in a way that changes the endpoint distance function monotonically The algorithms rely on our recent theoretical results characterizing combinatorially the maximum of panel-and-hinge chains They allow us to reduce the list problem to finding a shortest path between two vertices in an associated simple triangulated polygon, and the last problem to a simple version of the planar carpenter's tide problem

关键词： Chains

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Finding the Jaccard Median

Finding the Jaccard Median

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chierichetti, Flavio Kumar, Ravi Pandey, Sandeep Vassilvitskii, Sergei Yahoo Res Sunnyvale CA USA

ISBN: (纸本)9780898717013

The median problem in the weighted Jaccard metric was analyzed by Spath in 1981. Up until now, only an exponential-time exact algorithm was known. We (a) obtain a PTAS for the weighted Jaccard median problem and (b) show that the problem does not admit a FPTAS (assuming P not equal NP), even when restricted to binary vectors The PTAS is built on a number of different algorithmic ideas and the hardness result makes use of an especially interesting gadget.

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