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

共 197 条记录，以下是61-70 订阅

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Solving Simple Stochastic Tail Games

Solving Simple Stochastic Tail Games

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gimbert, Hugo Horn, Florian CNRS LaBRI Bordeaux France IST Austria Klosterneuburg Austria Univ Paris 07 CNRS LIAFA F-75221 Paris 05 France

ISBN: (纸本)9780898717013

Infinite stochastic games ale a natural model for open reactive processes one player represents the controller and the other represents a hostile environment. The evolution of the system depends on the decisions of the players, supplemented by chance. There are two main algorithmic problems on such games: computing the values of the vertices (quantitative analysis) and deciding whether a player can win with probability one, or arbitrarily close to one (qualitative analysis) In this paper, we reduce the quantitative analysis of simple stochastic tail games (where both players have perfect information and the winner does not depend on finite prefixes) to the qualitative analysis: we provide an algorithm computing values which uses qualitative analysis as a sub-procedure. The correctness proof of this algorithm reveals several nice properties of perfect-information stochastic tail games, in particular the existence of optimal strategies. We apply these results to games whose winning conditions are boolean combinations of mean-payoff and Buchi conditions

关键词： Stochastic systems

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Algorithms for ray class groups and Hilbert class fields

Algorithms for ray class groups and Hilbert class fields

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Eisentraeger, Kirsten Hallgren, Sean Penn State Univ Dept Math University Pk PA 16802 USA Penn State Univ Dept Comp Sci & Engn University Pk PA 16802 USA

ISBN: (纸本)9780898717013

This paper analyzes the complexity of problems from class field theory Class field theory can be used to show the existence of infinite families of number fields with constant root discriminant. Such families have been pi posed for use in lattice-based cryptography and for constructing error-correcting codes Little is known about the complexity of computing them. We show that computing the lay class group and computing certain subfields of Hilbert class fields efficiently reduce to known computationally difficult problems. These include computing the unit group and class group, the principal ideal problem, factoring, and discrete log. As a consequence, efficient quantum algorithms for these problems exist in constant degree number fields

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Tree Embeddings for Two-Edge-Connected Network Design

Tree Embeddings for Two-Edge-Connected Network Design

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Gupta, Anupam Krishnaswamy, Ravishankar Ravi, R. Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

ISBN: (纸本)9780898717013

The group Steiner problem is a classical network design problem where we are given a graph and a collection of groups of vertices, and want to build a min-cost subgraph that connects the root vertex to at least one vertex from each group What, if we wanted to build a subgraph that two-edge-connects the root to each group that is, for every group g subset of V, the subgraph should contain two edge-disjoint paths from the root to some vertex in g? What if we wanted the two edge-disjoint paths to end up at distinct vertices in the group, so that the loss of a single member of the group would not destroy connectivity? In this paper, we investigate tree-embedding techniques that can be used to solve these and other 2-edge-connected network design problems. We illustrate the potential of these techniques by giving poly-logarithmic approximation algorithms for two-edge-connected versions of the group Steiner, connected facility location, buy-at-bulk, and the k-MST problems.

关键词： Approximation algorithms

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Incentive Compatible Budget Elicitation in Multi-unit Auctions

Incentive Compatible Budget Elicitation in Multi-unit Auctio...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Bhattacharya, Sayan Conitzer, Vincent Munagala, Kamesh Xia, Lirong Duke Univ Dept Comp Sci Durham NC 27706 USA

ISBN: (纸本)9780898717013

In this paper, we consider the problem of designing incentive compatible auctions lot multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints When only the valuations ale private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentive-compatible auction achieving Pareto-optimality They further show that this auction is not truthful with private budgets, so that there is no deterministic Pareto-optimal auction with private budgets Our main contribution is to show the following Budget Monotonicity property of this auction When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget. smaller than the truth This implies that the adaptive clinching auction is incentive compatible when over-reporting the budget, is not possible (for instance, when funds must be shown upfront) We can also make reporting larger budgets suboptimal with a small randomized modification to the auction In either case, this makes the modified auction Pareto-optimal with private budgets We also show that the Budget Monotonicity property does not hold for auctioning indivisible units of the good, showing a sharp contrast between the divisible and indivisible cases The Budget Monotonicity property also Implies other unproved results in tins context For revenue maximization: the same auction improves the best-known competitive ratio due to Abrams [1] by a factor of 4, and asymptotically approaches the performance of the optimal single-price auction Finally, we consider the problem of revenue maximization (or social welfare) in a Bayesian setting We allow the bidders have public size constraints (on the amount of good they are willing to buy) in addition to private budget, constraints We show a. simple poly-time computable 5 83-approximation to the optimal Bayesian incentive compatible mechanism, that is implementable in dominant strategies Our tec

关键词： Budget control

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On the possibility of faster SAT algorithms

On the possibility of faster SAT algorithms

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Patrascu, Mihai Williams, Ryan AT&T Labs Florham Pk NJ USA IBM Corp Almaden Res Ctr San Jose CA 95120 USA

ISBN: (纸本)9780898717013

We describe reductions from the problem of determining the satisfiability of Boolean CNF formulas (CNF-SAT) to several natural algorithmic problems. We show that attaining any of the following bounds would improve the state of the art in algorithms for SAT an O(n(k-epsilon)) algorithm for k-DOMINATING SET, for any k >= 3, a (computationally efficient) protocol for 3-party set disjointness with o(m) bits of communication, an n(o(d)) algorithm for d-SUM, an O(n(2-epsilon)) algorithm for 2-SAT formulas with m = n(1+o(1)) clauses, where two clauses may have unrestricted length, and an O((n + m)(k-epsilon)) algorithm for HornSat with k unrestricted length clauses. One may interpret our reductions as new attacks on the complexity of SAT, or sharp lower bounds conditional on exponential hardness of SAT.

关键词： Boolean algebra

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Rumour spreading and graph conductance

Rumour spreading and graph conductance

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chierichetti, Flavio Lattanzi, Silvio Panconesi, Alessandro Univ Roma La Sapienza Dipartimento Informat Rome Italy

ISBN: (纸本)9780898717013

We show that if a connected graph with n nodes has conductance phi then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log(4) n/phi(6)) many steps, with high probability, using the PUSH-PULL strategy. An interesting feature of our approach is that it draws a connection between rumour spreading and the spectral sparsification procedure of Spielman and Teng [23].

关键词： Graph theory

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Correlation Robust Stochastic Optimization

Correlation Robust Stochastic Optimization

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Agrawal, Shipra Ding, Yichuan Saberi, Amin Ye, Yinyu Stanford Univ Stanford CA 94305 USA Management Sci & Engn Elect Engn Stanford CA 94305 USA

ISBN: (纸本)9780898717013

We consider a robust model proposed by Scarf, 1958, for stochastic optimization when only the marginal probabilities of (binary) random variables are given, and the correlation between the random variables is unknown. In the robust model, the objective is to minimize expected cost against worst possible joint distribution with those marginals. We introduce the concept of correlation gap to compare this model to the stochastic optimization model that ignores correlations and minimizes expected cost under independent Bernoulli distribution We identify a class of functions, using concepts of summable cost sharing schemes from game theory, for which the correlation gap is well-bounded and the robust model can be approximated closely by the independent distribution model. As a result, we derive efficient approximation factors for many popular cost functions, like submodular functions, facility location, and Steiner tree. As a byproduct, our analysis also yields some new results in the areas of social welfare maximization and existence of Walrasian equilibria, which may be of independent interest.

关键词： Game theory

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Optimally Reconstructing Weighted Graphs Using Queries

Optimally Reconstructing Weighted Graphs Using Queries

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Mazzawi, Hanna Technion Israel Inst Technol IL-32000 Haifa Israel

ISBN: (纸本)9780898717013

In this paper, we consider the problem of reconstructing a hidden graph with in edges using additive queries Given a graph G = (V, E) and a set of vertices S subset of V, an additive query. Q(S), asks for the number of edges in the subgraph induced by S. The information theoretic lower bound for the query complexity of reconstructing a graph with n vertices and in edges is Omega (m log n(2)/m/log m) In this paper we give the first polynomial time algorithm with query complexity that matches this lower bound(1) This solves the open problem by [S. Choi and J. Han Kim. Optimal Query Complexity-Bounds for Finding Graphs. STOC, 749-758, 2008] In the paper, we actually show an algorithm for the generalized problem of reconstructing weighted graphs. In the weighted case, an additive query, Q(S), asks for the sum of weights of edges in the subgraph induces by S The complexity of the algorithm also matches the information theoretic lower bound.

关键词： Graphic methods

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Fast distance multiplication of unit-Monge matrices

Fast distance multiplication of unit-Monge matrices

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Tiskin, Alexander Univ Warwick Dept Comp Sci Coventry CV4 7AL W Midlands England

ISBN: (纸本)9780898717013

Monge matrices play a fundamental role in optimisation theory, graph and string algorithms Distance multiplication of two Monge matrices of size n can be performed in time O(n(2)). Motivated by applications to string algorithms, we introduced in previous works a subclass of Monge matrices, that we call simple unit-Monge matrices. We also gave a distance multiplication algorithm for such matrices, running in time O(n(15)). Landau asked whether this problem can be solved in linear time. In the current work, we give an algorithm running in time 0(n log thus approaching an answer to Landau's question within a logarithmic factor. The new algorithm implies immediate improvements in running time for a number of algorithms on strings and graphs. In particular, we obtain an algorithm for finding a maximum clique in a circle graph in time 0(n log(2) n), and a surprisingly efficient algorithm for comparing compressed strings. We also point to potential applications in group theory, by making a connection between unit-Monge matrices and Coxeter monoids We conclude that unit-Monge matrices are a fascinating object and a powerful tool, that deserves further study from both the mathematical and the algorithmic viewpoints.

关键词： Group theory

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Partition constrained covering of a symmetric crossing supermodular function by a graph

Partition constrained covering of a symmetric crossing super...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Bernath, Attila Grappe, Roland Szigeti, Zoltan Eotvos Lorand Univ Dept Operat Res Egervary Res Grp MTA ELTE Pazmeny Peter Setany 1-C H-1117 Budapest Hungary Univ Paris 13 Sorbonne Paris Cite LIPN CNRS UMR 7030 F-93430 Villetaneuse France UJF Grenoble INP CNRS Lab G SCOP F-38000 Grenoble France

ISBN: (纸本)9780898717013

Given a symmetric crossing super modular set function p on V and a partition P of V, we solve the problem of finding a graph with ground set V having edges only between the classes of P such that for every subset X of V the cut of the graph defined by X contains at least p(X) edges. The objective is to minimize the number of edges of the graph This problem is a common generalization of the global edge-connectivity augmentation of a graph with partition constraints, which was solved by Bang-Jensen, Gabow, Jordan and Szigeti [1] and the problem of covering a. symmetric crossing supermodular set function solved by Benezur and Frank [3] Our problem can be considered as an abstract form of the problem of global edge-connectivity augmentation of a hypergraph by a multipartite graph;which was earlier solved by the authors [5]

关键词： Set theory

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