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Distributed PageRank Computation with Link Failures

Distributed PageRank Computation with Link Failures

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2009 American Control Conference (ACC 2009)

作者： Hideaki Ishii Roberto Tempo Department of Computational Intelligence and Systems Science Tokyo Institute of Technology 4259-J2-54 Nagatsuta-cho Midori-ku Yokohama 226-8502 Japan IEIIT-CNR Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy

ISBN: (纸本)9781424445233

The Google search engine employs the so-called PageRank algorithm for ranking the search results. This algorithm quantifies the importance of each web page based on the link structure of the web. In this paper, we continue our recent work on distributed randomized computation of PageRank, where the pages locally determine their values by communicating with linked pages. In particular, we propose a distributed randomized algorithm with limited information, where only part of the linked pages is required to be contacted. This is useful to enhance flexibility and robustness in computation and communication.

关键词： Distributed computation Link failures Multi-agent consensus PageRank algorithm Randomization Stochastic matrices Search engines arithmetic Web pages Distribute COMMUNICATING Web search engines randomized algorithms Flexibility Communication Research

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A random coordinate descent method for large-scale resource allocation problems

A random coordinate descent method for large-scale resource ...

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IEEE Annual Conference on Decision and Control

作者： I. Necoara University Politehnica Bucharest Automatic Control and Systems Engineering Department

ISBN: (纸本)9781467320658

In this paper we develop a randomized (block) coordinate descent method for solving singly linear equality constrained optimization problems that appear for example in resource allocation over networks. We show that for strongly convex objective functions the new algorithm has an expected linear convergence rate that depends on the second smallest eigenvalue λ_2(Q) of a matrix Q that is defined in terms of the probabilities and the number of blocks. However, the computational complexity per iteration of our method is much simpler than of a method based on full gradient information. We also focus on how to choose the probabilities to make this randomized algorithm to converge as fast as possible and we arrive at solving a sparse SDP. Finally, we present some numerical results for our method that show its efficiency on huge sparse problems.

关键词： descent method Resource utilization management of resources randomized algorithms Coordinates iterative methods Converge

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Optimal Column-Based Low-Rank Matrix Reconstruction 12

Optimal Column-Based Low-Rank Matrix Reconstruction

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Venkatesan Guruswami Ali Kemal Sinop Computer Science Department Carnegie Mellon University

ISBN: (纸本)9781611972108

We prove that for any real-valued matrix X ∈ R~(m×n), and positive integers r ≥ k, there is a subset of r columns of X such that projecting X onto their span gives a {the square rot of}((r＋1)/(r-k＋1)) approximation to best rank-k approximation of X in Frobenius norm. We show that the trade-off we achieve between the number of columns and the approximation ratio is optimal up to lower order terms. Furthermore, there is a deterministic algorithm to find such a subset of columns that runs in O(rnm~ω logm) arithmetic operations where ω is the exponent of matrix multiplication. We also give a faster randomized algorithm that runs in O(rnm~2) arithmetic operations.

关键词： Matrix multiplication FOOT SUPPORT Subset deterministic algorithms Euclidean matrix norm Exponent arithmetic Optimal matrices mechanical heart valve approximation randomized algorithms Surgery

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Online Degree-Bounded Steiner Network Design 16

Online Degree-Bounded Steiner Network Design

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Sina Dehghani Soheil Ehsani MohammadTaghi Hajiaghayi Vahid Liaghat University of Maryland Stanford University

ISBN: (纸本)9781510819672

We initiate the study of degree-bounded network design problems in the online setting. The degree-bounded Steiner tree problem - which asks for a subgraph with minimum degree that connects a given set of vertices - is perhaps one of the most representative problems in this class. This paper deals with its well-studied generalization called the degree-bounded Steiner forest problem where the connectivity demands are represented by vertex pairs that need to be individually connected. In the classical online model, the input graph is given offline but the demand pairs arrive sequentially in online steps. The selected subgraph starts off as the empty subgraph, but has to be augmented to satisfy the new connectivity constraint in each online step. The goal is to be competitive against an adversary that knows the input in advance. The standard techniques for solving degree bounded problems often fall in the category of iterative and dependent rounding techniques. Unfortunately, these rounding methods are inherently difficult to adapt to an online settings since the underlying fractional solution may change dramatically in between the rounding steps. Indeed, this might be the very reason that despite many advances in the online network design paradigm in the past two decades, the natural family of degree bounded problems has remained widely open. In this paper, we design an intuitive greedy-like algorithm that achieves a competitive ratio of O(log n) where n is the number of vertices. We show that no (randomized) algorithm can achieve a (multiplicative) competitive ratio o(log n); thus our result is asymptotically tight. We further show strong hardness results for the group Steiner tree and the edge-weighted variants of degree-bounded connectivity problems. Furer and Raghavachari resolved the offline variant of degree-bounded Steiner forest in their paper in SODA'92. Since then, the family of degree-bounded network design problems has been extensively studied in the litera

关键词： network design problem Steiner trees Steiner network rounding on-line model OFF LINE randomized algorithms vertex head paper family

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A polylogarithmic space deterministic streaming algorithm for approximating distance to monotonicity 15

A polylogarithmic space deterministic streaming algorithm fo...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Timothy Naumovitz Michael Saks Department of Mathematics Rutgers University

ISBN: (纸本)9781510813311

The distance to monotonicity of a sequence of n numbers is the minimum number of entries whose deletion leaves an increasing sequence. We give the first deterministic streaming algorithm that approximates the distance to monotonicity within a 1 + ε factor for any fixed ε > 0 and runs in space polylogarithmic in the length of the sequence and the range of the numbers. The best previous deterministic algorithm achieving the same approximation factor required space Ω(n~(1/2)) [9]. Previous polylogarithmic space algorithms were either randomized [10], or had approximation factor no better than 2 [8]. We also present space lower bounds for this problem: Any deterministic streaming algorithm that gets a 1 + ε approximation requires space Ω(1/ε log~2(n)) and any randomized algorithm requires space Ω(1/ε(log~2(n))/(log log(n))).

关键词： monotonicity Streaming increasing sequence deterministic randomized algorithms Lower bound algorithms total number of arm entries approximation entry

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Online Pricing with Impatient Bidders 16

Online Pricing with Impatient Bidders

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Marek Cygan Marcin Mucha Piotr Sankowski Qiang Zhang Institute of Informatics University of Warsaw

ISBN: (纸本)9781510819672

In this paper we consider the following online pricing problem. An auctioneer is selling identical items in unlimited supply, whereas each bidder from a given set is interested in purchasing a single copy of the item. Each bidder is characterized by a budget and a time interval, in which he is considering to buy the item. Bidders are willing to buy the item at the earliest time provided it is within their time intervals and the price at that time is within their budgets. We call such bidders impatient bidders. The problem is considered in the online setting, i.e., each bidder arrives at the start of his time interval, and only then an algorithm learns of his existence and his budget. The goal of the seller is to set the price of the item over time so that the total revenue is maximized. We study two versions of the impatient bidders problem: the one introduced by Bansal et al. [TALG'10], and a more restricted setting in which the deadline of each bidder remains unknown until it is hit. We give tight bounds for both settings. Rather surprisingly, in both cases the optimum competitive ratios are the same. In particular we prove that the competitive ratio of an optimum deterministic algorithm is Θ(log h/log log h), whereas for randomized algorithms it is Θ(log log h).

关键词： Time intervals Budgets Pricing randomized algorithms solidification Histidine Auctioneers deterministic algorithms

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Minimizing Inputs for Strong Structural Controllability

Minimizing Inputs for Strong Structural Controllability

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American Control Conference

作者： Kumar Yashashwi Shana Moothedath Prasanna Chaporkar Indian Institute of Technology Bomhay India University of Washington USA

ISBN: (纸本)9781538679012;9781538679265

The notion of strong structural controllability (s-controllability) allows for determining controllability properties of large linear time-invariant systems even when numerical values of the system parameters are not known a priori. The s-controllability guarantees controllability for all numerical realizations of the system parameters. We address the optimization problem of minimal cardinality input selection for s-controllability. Previous work shows that not only the optimization problem is NP-hard, but finding an approximate solution is also hard. We propose a randomized algorithm using the notion of zero forcing sets to obtain an optimal solution with high probability. We compare the performance of the proposed algorithm with a known heuristic [1] for synthetic random systems and three real world networks, viz. IEEE 39-bus system, protein-protein interaction network, and US airport network. It is found that our algorithm performs much better than the heuristic in each of these cases.

关键词： system parameter structural controllability controllability randomized algorithms Heuristics numerical value Nondeterministic polynomial-time hard optimal solution

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Four Soviets Walk the Dog - with an Application to Alt's Conjecture 14

Four Soviets Walk the Dog - with an Application to Alt's Con...

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Annual ACM-SIAM Symposium on Discrete algorithms

作者： Kevin Buchin Maike Buchin Wouter Meulemans Wolfgang Mulzer TU Eindhoven The Netherlands Ruhr Universität Bochum Germany Freie Universität Berlin Germany

ISBN: (纸本)9781611973389

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Frechet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original O(n~2log n) algorithm by Alt and Godau for computing the Frechet distance remains the state of the art (here n denotes the number of vertices on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUM-hard. In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Frechet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Frechet distance between two polygonal curves in time O(n~2(log n)~(1/2)(log log n)~(3/2)) on a pointer machine and in time O(n~2(log log n)~2) on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth O(n~(2-ε)), for some ε > 0. This provides evidence that the decision problem may not be 3SUM-hard after all and reveals an intriguing new aspect of this well-studied problem.

关键词： Decision problem Conjecture state of the art Canis familiaris randomized algorithms Decision Trees

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Density and regularity theorems for semi-algebraic hypergraphs 15

Density and regularity theorems for semi-algebraic hypergrap...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Jacob Fox Janos Pach Andrew Suk Massachusetts Institute of Technology EPFL Lausanne and Courant Institute University of Illinois at Chicago

ISBN: (纸本)9781510813311

A k-uniform semi-algebraic hypergraph H is a pair (P, E), where P is a subset of R~d and E is a collection of k-tuples {p1,...,p_k} is contained in P such that (p_1,...,p_k) ∈ E if and only if the kd coordinates of the pi-s satisfy a boolean combination of a finite number of polynomial inequalities. The complexity of H can be measured by the number and the degrees of these inequalities and the number of variables (coordinates) kd. Several classical results in extremal hypergraph theory can be substantially improved when restricted to semialgebraic hypergraphs. Substantially improving a theorem of Fox, Gromov, Lafforgue, Naor, and Pach, we establish the following "polynomial regularity lemma": For any 0 < ε < 1/2, the vertex set of every k-uniform semi-algebraic hypergraph H = (P, E) can be partitioned into at most (1/ε)~c parts P_1, P_2,..., as equal as possible, such that all but at most an ε-fraction of the k-tuples of parts (P_(i_1),..., P_(i_k)) are homogeneous in the sense that either every k-tuple (p_(i_1),...p_(i_k)) ∈ P_(i_1) × ... × P_(i_k) belongs to E or none of them do. Here c > 0 is a constant that depends on the complexity of H. We also establish an improved lower bound, single exponentially decreasing in k, on the best constant δ > 0 such that the vertex classes P_1,..., P_k of every k-partite k-uniform semi-algebraic hypergraph H = (P_1 ∪...∪ P_k, E) with |E| ≥ εΠ_(j=1)~k |P_i| have, for 1 ≤ i ≤ k, δ|P_i|-element subsets P'_i is contained in P_i satisfying P'_1 × ... × P'_k is contained in E. The best previously known lower bound on δ due to Bukh and Hubard decreased double exponentially fast in k. We give three geometric applications of our results. In particular, we establish the following strengthening of the so-called same-type lemma of Barany and Valtr: Any disjoint finite sets P_1,..., P_k is contained in R~d (k > d) have for 1 ≤ i ≤ k subsets P'_i of size at least 2~(-O(d~3k log k))|P_i| with the property that every k-tuple formed by taking on

关键词： hypergraph Hydrogen CIRCUIT TO PRESSURE CONVERTER Theorem instruction type randomized algorithms inequalities

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Finding duplicates in a data stream 09

Finding duplicates in a data stream

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Parikshit Gopalan Jaikumar Radhakrishnan University of Washington & Microsoft Research SVC TIFR

Given a data stream of length n over an alphabet [m] where n > m, we consider the problem of finding a duplicate in a single pass. We give a randomized algorithm for this problem that uses O((logm)~3) space. This answers a question of Muthukrishnan [Mut05] and Tarui [Tar07], who asked if this problem could be solved using sub-linear space and one pass over the input. Our algorithm solves the more general problem of finding a positive frequency element in a stream given by frequency updates where the sum of all frequencies is positive. Our main tool is an Isolation Lemma that reduces this problem to the task of detecting and identifying a Dictatorial variable in a Boolean halfspace. We present various relaxations of the condition n > m, under which one can find duplicates efficiently.

关键词： FINDINGS data flow randomized algorithms sublinear streams one pass

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