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

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Classified Stable Matching

Classified Stable Matching

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Huang, Chien-Chung Max Planck Inst Informat D-66123 Saarbrucken Germany

ISBN: (纸本)9780898717013

We introduce the CLASSIFIED STABLE MATCHING problem, a problem motivated by academic hiring. Suppose that a number of Institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences over the other side An institute classifies the applicants based on their research areas (or any other criterion), and, for each class, it sets a lower bound and an upper bound on the number of applicants it would hire in that class. The objective is to find a stable matching from which no group of participants has reason to deviate. Moreover, the matching should respect the upper/lower bounds of the classes. In the first part of the paper, we study classified stable matching problems whose classifications belong to a fixed set of "order types." We show that if the set consists entirely of downward forests, there is a polynomial-time algorithm, otherwise, it is NP-complete to decide the existence of a stable matching. In the second part, we investigate the problem using a polyhedral approach. Suppose that all classifications are laminar families and there is no lower bound. We propose a set of linear inequalities to describe stable matching polytope and prove that it is integral. This integrality result allows us to find optimal stable matchings in polynomial time using Ellipsoid algorithm;furthermore, it gives a description of the stable matching polytope for the many-to-rummy (unclassified) stable matching problem, thereby answering an open question posed by Sethuraman, Teo and Qian.

关键词： Polynomial approximation

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A Fourier space algorithm for solving quadratic assignment problems

A Fourier space algorithm for solving quadratic assignment p...

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Kondor, Risi CALTECH Ctr Math Informat Pasadena CA 91125 USA

ISBN: (纸本)9780898717013

The quadratic assignment problem (QAP) is a central problem in combinatorial optimization Several famous computationally hard tasks, such as graph matching, partitioning, and the traveling salesman all reduce to special cases of the QAP. In this paper we propose a new approach to the QAP based on the theory of non commutative Fourier analysis on the symmetric group Specifically, we present a branch and bound algorithm that performs both the branching and the bounding steps in Fourier space. By exploiting the band limited nature of the QAP objective function and using FFT techniques, the algorithm runs in O(n(3)) time per branch and bound node. The techniques underlying the algorithm generalize to a range of other combinatorial optimization problems.

关键词： Combinatorial optimization

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Lower bounds for Edit Distance and Product Metrics via Poincare-Type Inequalities

Lower bounds for Edit Distance and Product Metrics via Poinc...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Andoni, Alexandr Jayram, T. S. Patrascu, Mihai Princeton U CCT Princeton NJ 08541 USA IBM Almaden Armonk NY 10504 USA AT&T Labs Florham Pk NJ 07748 USA

ISBN: (纸本)9780898717013

We prove that any sketching protocol for edit distance achieving a constant approximation regimes nearly logarithmic (in the strings' length) communication complexity This is an exponential improvement over the previous, doubly-logarithmic, lower bound of [Andoni-Krauthgamer, FOCS'07] Our lower bound also applies to the Ulam distance (edit distance over non-repetitive strings) In this special case, it is polynomially related to the recent, upper bound of [Andoni-Indyk-Krauthgamer, SODA'09]. From a technical perspective, we prove a. direct-sum theorem for sketching product metrics that is of independent interest, We show that, for any metric X that requires sketch size which is a sufficiently large constant, sketching the max-product metric l(infinity)(d)(X) requires Omega(d) bits. The conclusion, in fact, also holds for arbitrary two-way communication The proof uses a novel technique Lot information complexity based on Poincare inequalities and suggests an intimate connection between non-embeddability, sketching and communication complexity

关键词： Computational complexity

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Distributed Agreement with Optimal Communication Complexity

Distributed Agreement with Optimal Communication Complexity

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gilbert, Seth Kowalski, Dariusz R. Ecole Polytech Fed Lausanne Lausanne Switzerland Univ Liverpool Liverpool Merseyside England

ISBN: (纸本)9780898717013

We consider the problem of fault-tolerant agreement in a crash-prone synchronous system. We present a new randomized consensus algorithm that achieves optimal communication efficiency, using only O(n) bits of communication, and terminates in (almost optimal) time O(logn), with high probability. The same protocol, with minor modifications, can also be used in partially synchronous networks, guaranteeing correct behavior even in asynchronous executions, while maintaining efficient performance in synchronous executions. Finally, the same techniques also yield a randomized, fault-tolerant gossip protocol that terminates in O(log*n) rounds using O(n) messages (with bit complexity that depends on the data being gossiped).

关键词： Complex networks

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On the Exact Space Complexity of Sketching and Streaming Small Norms

On the Exact Space Complexity of Sketching and Streaming Sma...

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Kane, Daniel M. Nelson, Jelani Woodruff, David P. Harvard Univ Dept Math Cambridge MA 02138 USA

ISBN: (纸本)9780898717013

We settle the 1-pass space complexity of (1 +/- epsilon)- approximating the L-p norm, for real p with 1 <= p <= 2, of a length-n vector updated in a length-in stream with updates to its coordinates. We assume the updates are integers in the range ( M, M]. In particular, we show the space required is Theta(epsilon(-2) log(mM) + log log(n)) bits. Our result also holds for 0 < p < 1;although L-p is not a norm in this case, it remains a well-defined function. Our upper bound improves upon previous algorithms of [Indyk, JACM '06] and [Li, SODA '08]. This improvement comes from showing an improved derandomization of the Lp sketch of Indyk by using k-wise independence for small k, as opposed to using the heavy hammer of a generic pseudorandom generator against space-bounded computation such as Nisan's PRO Our lower bound improves upon previous work of [Alon-Matias-Szegedy, JCSS '99] and [Woodruff, SODA '04], and is based on showing a direct sum property for the 1-way communication of the gap-Hamming problem.

关键词： Vector spaces

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Compact Ancestry Labeling Schemes for XML Trees

Compact Ancestry Labeling Schemes for XML Trees

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Fraigniaud, Pierre Korman, Amos CNRS F-75700 Paris France

ISBN: (纸本)9780898717013

An ancestry labeling scheme labels the nodes of any Lice in such a way that ancestry queries between any two nodes can be answered Just by looking at then corresponding labels The common measure to evaluate, the quality of an ancestry scheme is by as label size, that, is the maximum number of bits stored in a label, taken over all n-node trees The design of ancestry labeling schemes finds applications in XML search engines In these contexts, even small improvements in the label size are important, As a result, following the proposal of a. simple interval based ancestry scheme with label size 2 log n bits (Kannan et al., STOC 88), a considerable amount;of work was devoted to improve the bound on the label size The cut rent state of the ail: upper bound is log + O(root log n) bits (Abiteboul el al, SICOMP 06) which is still far from the known log n + Omega (log log n) lower bound (Alstrup et al SODA 03) Motivated by the fact that typical XML. trees have extremely small depth, this paper parameterizes the quality measure of an ancestry scheme not, only by the number of nodes in the given tree but also by its depth Out main result is the construction of an ancestry scheme that labels n-node trees of depth d with labels of size log n + 2 log d O(1). In addition to our main result, we prove a result, that;may be of independent interest concerning the existence of a. small universal graph for the family of trees with bounded depth

关键词： Search engines

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Data-Specific Analysis of String Sorting

Data-Specific Analysis of String Sorting

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Seidel, Raimund Univ Saarland Fachrichtung Informat D-66123 Saarbrucken Germany

ISBN: (纸本)9780898717013

We consider the complexity of sorting, strings in the model that counts comparisons between symbols and not Just comparisons between strings We show that lot any set, of strings S the complexity of sorting S can naturally be expressed in terms of the trie induced by S This holds not only for lower bounds but also 1:01 the running tunes of various algorithms Thus this "data-specific" analysis allows a direct comparison of different algorithms running on the same data We give such "data-specific" analyses for various versions of quicksort and versions of mergesort As a corollary we arrive at a very simple analysis of quicksorting random strings, which so flu required rather sophisticated mathematical tools As part of this we provide insights in the analysis of tries of random strings which may be interesting in then own right

关键词： Sorting

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Paired Approximation Problems and Incompatible Inapproximabilities

Paired Approximation Problems and Incompatible Inapproximabi...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Eppstein, David Univ Calif Irvine Dept Comp Sci Irvine CA 92717 USA

ISBN: (纸本)9780898717013

This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems In many instances, it is possible to efficiently find an approximation of this type that is better than known inapproximability lower bounds for either of the two individual optimization problems forming the pair In particular, we find either a (1 + epsilon)-approximation to (1,2)-TSP or a 1/epsilon-approximation to maximum independent set, from a. given graph, in linear time We show a similar paned approximation result for finding either a coloring or a long path However, no such tradeoff exists in some the cases for set cover and hitting set problems defined from a single set family, and for clique and independent set, problems on the same graph, it is not possible to find an approximation when both problems are combined that is better than the best approximation km either problem on its own

关键词： Optimization

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Thin Partitions: Isoperimetric Inequalities and a Sampling Algorithm for Star Shaped Bodies

Thin Partitions: Isoperimetric Inequalities and a Sampling A...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chandrasekaran, Karthekeyan Dadush, Daniel Vempala, Santosh Georgia Inst Technol Atlanta GA 30332 USA

ISBN: (纸本)9780898717013

Star-shaped bodies at e an important nonconvex generalization of convex bodies (e g linear programming with violations) Here we present, an efficient algorithm for sampling a given star-shaped body complexity of the algorithm grows polynomially in the dimension and inverse polynomially in the fraction of the volume taken up by the kernel of the star-shaped body analysis is based on a new isoperimetric inequality Our main technical contribution is a tool for proving such inequalities when the domain is not convex As a consequence, we obtain a polynomial algorithm kit computing the volume of such a set as well In contrast, linear optimization over star-shaped sets is NP-hard.

关键词： Linear programming

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Quantum algorithms for highly non-linear Boolean functions

Quantum algorithms for highly non-linear Boolean functions

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Roetteler, Martin NEC Labs Amer Princeton NJ 08540 USA

ISBN: (纸本)9780898717013

Attempts to separate the power of classical and quantum models of computation have a long history The ultimate goal is to find exponential separations for computational problems However, such separations do not come a dime a dozen while there were some wily successes in the form Of hidden subgroup problems for abelian groups winch generalize Shor's factoring algorithm perhaps most faithfully-only I'm a handful of non-abelian groups efficient quantum algorithms were found Recently, problems have gotten increased attention that seek to identify hidden sub-structures of other combinatorial and algebraic objects besides groups In this paper we provide new examples for exponential separations by considering hidden shift problems that are defined for several classes of highly non-linear Boolean functions These so-called bent functions arise in cryptography: where then property of having per reedy flat, Fourier spectra on the Boolean hypercube gives them resilience against certain types of attack We present new quantum algorithms that solve the hidden shift problems for several well classes of bent functions in polynomial time and with a constant number of queues, while the classical query complexity is shown to be exponential Our approach uses a technique that exploits the duality between bent functions and their Fourier transforms

关键词： Separation

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