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

共 197 条记录，以下是81-90 订阅

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Highway Dimension, Shortest Paths, and Provably Efficient, Algorithms

Highway Dimension, Shortest Paths, and Provably Efficient, A...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Abraham, Ittai Fiat, Amos Goldberg, Andrew V. Werneck, Renato F. Microsoft Research Silicon Valley United States Tel-Aviv University Israel

ISBN: (纸本)9780898717013

Computing driving directions has motivated many shortest path heuristics that, answer queries on continental scale networks, with tens of millions of intersections, literally instantly, and with very low storage over head In this paper we complement the experimental evidence with the first rigorous proofs of efficiency for many of the heuristics suggested over the past decade. We introduce the notion of highway dimension and show how low highway dimension gives a unified explanation for several seemingly different algorithms

关键词： Graph theory

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On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic

On Brambles, Grid-Like Minors, and Parameterized Intractabil...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Kreutzer, Stephan Tazari, Siamak Univ Oxford Oxford OX1 2JD England Humboldt Univ Berlin Germany

ISBN: (纸本)9780898717013

Brambles were introduced as the dual notion to treewidth, one of the most;central concepts of the graph minor theory of Robertson and Seymour. Recently, Grohe and Marx showed that there are graphs., in which every bramble of order larger than the square root of the treewidth is of exponential size in vertical bar G vertical bar On the positive side, they show the existence of polynomial-sized brambles of the older of the square root of the treewidth, up to log factors. We provide the first polynomial time algorithm to construct a. bramble in general graphs and achieve tins bound, up to log-factors We use this algorithm to construct grid-like minors, a replacement;structure for grid-minors recently introduced by Reed and Wood, in polynomial time Using the grid-like minors, we introduce the notion of a. perfect;bramble and an algorithm to find one in polynomial time Perfect hi ambles are brambles with a particularly simple structure and they also provide us with a subgraph that has bounded degree and still large treewidth. we use them to obtain a meta-theorem on deciding certain parameterized subgraph-closed problems on general graphs in time singly exponential in the parameter, the only other result with a similar flavor that is known to us is due to Demaine and Hajiaghayi and obtains a doubly- exponential bound on the parameter (albeit, for a more general class of parameterized problems). The second part of our work deals with providing a lower bound to Courcelle's famous theorem from almost two decades ago, stating that every graph property that Call be expressed by a sentence in monadic second-order logic (MSO), can be decided by a linear time algorithm on classes of graphs of bounded treewidth Whereas much work has been done on designing, improving, and applying algorithms on graphs of bounded treewidth, not much is known on the side of lower bounds what bound on the treewidth of a class of graphs "forbids" polynomial-time parameterized algorithms to decide MSO-s

关键词： Graphic methods

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Decomposition, Approximation, and Coloring of Odd-Minor-Free Graphs

Decomposition, Approximation, and Coloring of Odd-Minor-Free...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Demaine, Erik D. Hajiaghayi, MohammadTaghi Kawarabayashi, Ken-ichi MIT Comp Sci & Artificial Intelligence Lab 32 Vassar St Cambridge MA 02139 USA AT&T Labs Res Florham Pk NJ 07932 USA Natl Inst Informat Chiyoda Ku Tokyo 1018430 Japan

ISBN: (纸本)9780898717013

We prove two structural decomposition theorems about graphs excluding a fixed odd minor PI, and show how these theorems can be used to obtain approximation algorithms for several algorithmic problems in such graphs Our decomposition results provide new structural insights into odd-H-minor-free graphs, on the one hand generalizing the central structural result from Graph Minor Theory, and on the other hand providing an algorithmic decomposition into two bounded-treewidth graphs, generalizing a similar result for minors As one example of how these structural results conquer difficult problems, we obtain a polynomial-time 2-approximation for vertex coloring in odd-H-minor-free graphs, improving on the previous O(vertical bar V(H)vertical bar)-approximation for such graphs and generalizing the previous 2-approximation for H-minor-free graphs The class of odd-H-minor-free graphs is a vast generalization of the well-studied H-minor-free graph families and includes, for example, all bipartite graphs plus a bounded number of apices. Odd-H-minor-free graphs are particularly interesting from a structural graph theory perspective because they break away from the sparsity of H-minor-free graphs, permitting a quadratic number of edges.

关键词： Approximation algorithms

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One-Counter Markov Decision Processes

One-Counter Markov Decision Processes

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Brazdil, T. Brozek, V. Etessami, K. Kucera, A. Wojtczak, D. Masaryk Univ Fac Informat CS-60177 Brno Czech Republic Univ Edinburgh Sch Informat Edinburgh EH8 9YL Midlothian Scotland CWI Amsterdam Netherlands

ISBN: (纸本)9780898717013

We study the computational complexity of some central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs extend finite-state MDPs with an unbounded counter. The counter can be incremented, decremented, or not changed during each state transition, and transitions may be enabled or not depending on both the current state and on whether the counter value is 0 or not. Some states are "random", from where the next transition is chosen according to a given probability distribution, while other states are "controlled", from where the next transition is chosen by the controller. Different objectives for the controller give rise to different computational problems, aimed at computing optimal achievable objective values and optimal strategies. OC-MDPs are in fact equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a purely stochastic model heavily studied in queueing theory and applied probability. They can thus be viewed as a natural "adversarial" extension of a classic stochastic model. They can also be viewed as a natural probabilistic/controlled extension of classic one-counter automata. OC-MDPs also subsume (as a very restricted special case) a recently studied MDP model called "solvency games" that model a risk-averse gambling scenario. Basic computational questions for OC-MDPs include "termination" questions and "limit" questions, such as the following: does the controller have a strategy to ensure that the counter (which may, for example, count the number of jobs in the queue) will hit value 0 (the empty queue) almost surely (as.)? Or that the counter will have lint sup value co, as.? Or, that it will hit value 0 in a selected terminal state, a.s.? Or, in case such properties are not satisfied almost surely, compute their optimal probability over all strategies. We provide new upper and lower bounds on the complexity of such problems. Specifically,

关键词： Stochastic models

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Bidimensionality and Kernels

Bidimensionality and Kernels

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Fomin, Fedor V. Lokshtanov, Daniel Saurabh, Saket Thilikos, Dimitrios M. Univ Bergen Dept Informat N-5020 Bergen Norway Inst Math Sci CIT Campus Madras Tamil Nadu India Natl & Kapodistrian Univ Athens Dept Math Athens Greece

ISBN: (纸本)9780898717013

Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on H-minor free graphs Demaine and Hajiaghayi [SODA 2005] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this paper, we establish a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In parameterized complexity, each problem instance comes with a parameter k and the parameterized problem is said to admit a linear kernel if there is a polynomial time algorithm, called a kernelization algorithm, that reduces the input instance to an equivalent instance (called kernel) with size linearly bounded by k We show that "essentially" all bidimensional problems not only have sub-exponential time algorithms and PTASs but they also have linear kernels, affirmatively answering an open question from [J. ACM 2005] where the existence of linear kernels was conjectured for the first time In particular. we prove that every minor (respectively contraction) bidimensional problem that satisfies the separation property and is of finite integer index, admits a linear kernel for classes of graphs that exclude a fixed graph (respectively an apex graph H) H as a minor Recently, Bodlaender et al [FOCS 2009] laid the foundation for obtaining meta-algorithmic results for kernelization and showed that various problems satisfying some logical and compactness properties have polynomial, even linear kernels on graphs of bounded genus With the use of bidimensionality we are able to extend these results to minor-free and apex-minor-free graphs Our results imply that a multitude of bidimensional problems. which include DOMINATING SET, FEEDBACK VERTEX SET, EDGE DOMINATING SET, VERTEX COVER, r-DOMINATING SET, C

关键词： Graphic methods

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Online Learning with Queries

Online Learning with Queries

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chiang, Chao-Kai Lu, Chi-Jen Acad Sinica Inst Informat Sci Taipei Taiwan

ISBN: (纸本)9780898717013

The online learning problem requires a player to iteratively choose an action in an unknown and changing environment In the standard setting of this problem, the player has to choose an action in each round before knowing anything about the corresponding loss However, there are situations in which it seems possible for the player to spend efforts or resources to collect some prior information before her actions This motivates us to study a variant of the online learning problem, in which the player is allowed to query 13 bits horn the loss vector in each round before choosing her act ion Suppose each loss value is represented by K bits and distinct. loss values differ by at least some amount 6, and suppose diet e ale N actions to choose and T rounds to play We provide an algorithm rot this problem which achieves a regret of the following form Before 13 approaching B-1 = NK/2, the regret stays at O(root T ln N), and after B exceeding B-1 but before approaching B-2 = NK/2 + 3K/2-1 the regret chops slightly to O(root T ln N)/N), while after B exceeding B-2, the regret takes a dramatic drop to (N ln N)/delta Our algorithm is in fact close to optimal as we also provide regret lower bounds which almost match the regret upper bounds achieved by our algorithm

关键词： Drops

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A Max-Flow/Min-Cut Algorithm for a Class of Wireless Networks

A Max-Flow/Min-Cut Algorithm for a Class of Wireless Network...

引用

21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Yazdi, S. M. Sadegh Tabatabaei Savari, Serap A. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

ISBN: (纸本)9780898717013

The linear deterministic model of relay channels is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The max-flow/min-cut, theorem of Ford and Fulkerson has recently been extended to this wireless relay model This result was first proved by a random coding scheme over large blocks of transmitted signals We demonstrate the same result with a deterministic, polynomial-time algorithm which takes as input a single transmitted signal instead of a long block of signals. The max-flow/min-cut theorem of Ford and Fulkerson is related to a number of famous results in combinatorics including Hall's marriage theorem. Hall's marriage theorem is a special case of a well-known result in matroid theory and in transversal theory named the Rado-Hall theorem We show that the max-flow/min-cut theorem for linear deterministic relay networks is connected to (1) a two-dimensional transversal theorem for block matrices which is a new application of the Rado-Hall theorem and (2) a combinatorial result on sequences of block matrices which is obtained through results in submodular optimization

关键词： Wireless networks

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Counting Inversions, Offline Orthogonal Range Counting, and Related Problems

Counting Inversions, Offline Orthogonal Range Counting, and ...

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Chan, Timothy M. Patrascu, Mihai Univ Waterloo Cheriton Sch Comp Sci Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9780898717013

We give an O(n root lg n)-time algorithm for counting the number of inversions in a permutation on n elements This improves a long-standing previous bound of O(n lg n/ lg lg n) that followed from Dietz's data structure [WADS'89], and answers a question of Andersson and Petersson [SODA'95] As Dietz's result is known to be optimal for the related dynamic rank problem, our result demonstrates a significant improvement in the offline setting. Our new technique is quite simple: we perform a "vertical partitioning" of a trie (akin to van Elude Boas trees), and use ideas from external memory. However, the technique finds numerous applications for example, we obtain in d dimensions, an algorithm to answer n offline orthogonal range counting queries in time O(n lg(d-2+1/d) n);an improved construction time for online data structures for orthogonal range counting, an improved update time for the partial sums problem;faster Word RAM algorithms for finding the maximum depth in an arrangement of axis-aligned rectangles, and for the slope selection problem. As a bonus, we also give a simple (1 + epsilon)-approximation algorithm for counting inversions that runs in linear time, improving the previous O(n lg lg n) bound by Andersson and Petersson.

关键词： Data structures

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Differential Privacy in New Settings

Differential Privacy in New Settings

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Dwork, Cynthia Microsoft Research

ISBN: (纸本)9780898717013

Differential privacy is a recent notion of privacy tailored to the problem of statistical disclosure control how to release statistical information about a set;of people without compromising the the privacy of any individual [7] We describe new work [10, 9] that extends differentially private data analysis beyond the traditional setting of a trusted curator operating, in pelted, isolation, on a static dataset We ask How can we guarantee differential privacy, even against, an adversary that has access to the algorithm's Internal state, eg, by subpoena? An algorithm that achives this is said to be pan-private How can we guarantee differential privacy when the algorithm must continually produce outputs? We call this differential privacy under continual observation. We also consider these requirements in conjunction

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Synchrony and Asynchrony in Neural Networks

Synchrony and Asynchrony in Neural Networks

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21st Annual ACM/SIAM Symposium on Discrete Algorithms

作者： Kuhn, Fabian Panagiotou, Konstantinos Spencer, Joel Steger, Angelika Univ Lugano USI Fac Informat Lugano Switzerland Max Plank Inst Comp Sci Saarbrucken Germany Courant Inst Dept Comp Sci New York NY 10012 USA ETH Inst Theoret Comp Sci Zurich Switzerland

ISBN: (纸本)9780898717013

The dynamics of large networks is an important and fascinating problem. Key examples are the Internet, social networks, and the human brain. In this paper we consider a model introduced by DeVille and Peskin [6] for a stochastic pulse-coupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network This idealization has two benefits it captures essential features of neuronal behavior, and it allows the study of spontaneous synchronization, an important phenomenon in neuronal networks that is well-studied but unfortunately far from being well-understood In synchronous behavior the firing of one new on leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. In this paper we rigorously analyze their model In particular, by applying methods and tools that are frequently used in theoretical computer science, we provide a very precise picture of the dynamics and the evolution of the given system. In particular, we obtain insights into the coexistence of synchronous and asynchronous behavior and the conditions that trigger a "spontaneous" transition horn one state to another.

关键词： Neurons

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