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Maximum bipartite flow in networks with adaptive channel width

Maximum bipartite flow in networks with adaptive channel wid...

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36th International Colloquium on Automata, Languages and Programming

作者： Azar, Yossi Madry, Aleksander Moscibroda, Thomas Panigrahi, Debmalya Srinivasan, Aravind MIT Comp Sci & Artificial Intelligence Lab Stata Ctr Cambridge MA 02139 USA Tel Aviv Univ Sch Comp Sci IL-69978 Tel Aviv Israel Univ Maryland Dept Comp Sci College Pk MD 20742 USA Univ Maryland Inst Adv Comp Studies College Pk MD 20742 USA Microsoft Res Redmond WA 98052 USA

ISBN: (纸本)3642029299

Traditionally, network optimization problems assume that each link in the network has a fixed capacity. Recent research in wireless networking has shown that it is possible to design networks where the capacity of the links can be changed adaptively to suit the needs of specific applications. In particular, one gets a choice of having a few high capacity outgoing links or many low capacity ones at any node of the network. This motivates us to have a re-look at classical network optimization problems and design algorithms to solve them in this new framework. In particular, we consider the problem of maximum bipartite flow, which has been studied extensively in the fixed-capacity network model. One of the motivations for studying this problem arises from the need to maximize the throughput of an infrastructure wireless network comprising base-stations (one set of vertices in the bipartition) and clients (the other set of vertices in the bipartition). We show that this problem has a significantly different combinatorial structure in this new network model from the fixed-capacity one. While there are several polynomial time algorithms for the maximum bipartite flow problem in traditional networks, we show that the problem is NP-hard in the new model. In fact, our proof extends to showing that the problem is APX-hard. we complement our lower bound by giving two algorithms for solving the problem approximately. The first algorithm is deterministic and achieves an approximation factor of O(log N), where N is the number of nodes in the network, while the second algorithm is randomized and achieves an approximation factor of e/e-1. (C) 2010 Elsevier B.V. All rights reserved.

关键词： graph algorithm Maximum flow Linear program rounding Wireless networks Adaptive channel width

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New algorithms for a Simple Measure of Network Partitioning 17th

New Algorithms for a Simple Measure of Network Partitioning

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17th Annual Conference on Theory and Applications of Models of Computation (TAMC)

作者： Zhao, Xueyang Yan, Binghao Zhang, Peng Shandong Univ Sch Software Jinan 250101 Shandong Peoples R China

ISBN: (纸本)9783031203497;9783031203503

Partitioning a network into k pieces is a fundamental problem in network science. A simple measure of partitioning a network is provided by the Max k-Uncut problem. Given an n-vertex undirected graph G with nonnegative weights defined on edges, and a positive integer k, the Max k-Uncut problem asks to find a k-partition of the vertices of G to maximize the total weight of edges that are not in the cut. This problem is the complement of the classic Min k-Cut problem, and has close relation to many combinatorial optimization problems, including the famous Densest k-Subgraph problem. In this paper, we propose a greedy approximation algorithm for the Max k-Uncut problem with performance ratio 1 - 2(k-1)/n. The algorithm is very simple, which consists of only k - 1 min cut computations. The algorithm has fast running time O(kn(2)) and is hence implementable. The experimental results show that the algorithm has excellent practical performance.

关键词： Max k-Uncut Network partitioning graph algorithm Approximation algorithm Combinatorial optimization

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Memory-Aware Framework for Efficient Second-Order Random Walk on Large graphs 20

Memory-Aware Framework for Efficient Second-Order Random Wal...

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ACM SIGMOD International Conference on Management of Data (SIGMOD)

作者： Shao, Yingxia Huang, Shiyue Miao, Xupeng Cui, Bin Chen, Lei BUPT Beijing Key Lab Intelligent Telecommun Software Beijing Peoples R China Peking Univ Sch EECS Beijing Peoples R China Peking Univ Key Lab High Confidence Software Technol MOE Beijing Peoples R China Hong Kong Univ Sci & Technol Hong Kong Peoples R China

ISBN: (纸本)9781450367356

Second-order random walk is an important technique for graph analysis. Many applications use it to capture higher-order patterns in the graph, thus improving the model accuracy. However, the memory explosion problem of this technique hinders it from analyzing large graphs. When processing a billion-edge graph like Twitter, existing solutions (e.g., alias method) of the second-order random walk may take up 1796TB memory. Such high memory overhead comes from the memory-unaware strategies for node sampling across the graph. In this paper, to clearly study the efficiency of various node sampling methods in the context of second-order random walk, we design a cost model, and then propose a new node sampling method following the acceptance-rejection paradigm to achieve a better balance between memory and time cost. Further, to guarantee the efficiency of the second-order random walk within arbitrary memory budgets, we propose a memory-aware framework on the basis of the cost model. The framework applies a cost-based optimizer to assign desirable node sampling method for each node in the graph within a memory budget while minimizing the time cost. Finally, we provide general programming interfaces for users to benefit from the memory-aware framework easily. The empirical studies demonstrate that our memory-aware framework is robust with respect to memory and is able to achieve considerable efficiency by reducing 90% of the memory cost.

关键词： Random walk Memory efficient graph algorithm Large-scale

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Extension of Parallel Primitives and Their Applications to Large-Scale Data Processing 35th

Extension of Parallel Primitives and Their Applications to L...

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35th International Conference on Database and Expert Systems Applications (DEXA)

作者： Nakano, Masashi Chang, Qiong Miyazaki, Jun Tokyo Inst Technol Sch Comp Dept Comp Sci Tokyo Japan

ISBN: (纸本)9783031683114;9783031683121

Data parallel primitives are highly optimized general-purpose algorithms designed only for GPUs and are used as building blocks to develop applications. However, existing data parallel primitives cannot handle data larger than the GPU memory size. In this paper, we propose an extension to existing data parallel primitives to efficiently handle data larger than the GPU memory size by cooperatively using both GPUs and CPUs. Moreover, we evaluate the impact of these primitives when applying them to large data processing applications, with respect to both performance and software development cost.

关键词： GPU Data parallel primitives Database processing graph algorithm

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algorithmic Aspects of Disjunctive Domination in graphs 21st

Algorithmic Aspects of Disjunctive Domination in Graphs

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21st International Computing and Combinatorics Conference (COCOON)

作者： Panda, B. S. Pandey, Arti Paul, S. Indian Inst Technol Delhi Hauz Khas Dept Math New Delhi 110016 India Indian Stat Inst Adv Comp & Microelect Kolkata 700108 India

ISBN: (纸本)9783319213989;9783319213972

For a graph G = (V, E), a set D subset of V is called a disjunctive dominating set of G if for every vertex v is an element of V \ D, v is either adjacent to a vertex of D or has at least two vertices in D at distance 2 from it. The cardinality of a minimum disjunctive dominating set of G is called the disjunctive domination number of graph G, and is denoted by gamma(d)(2)(G). The MINIMUM DISJUNCTIVE DOMINATION PROBLEM (MDDP) is to find a disjunctive dominating set of cardinality gamma(d)(2)(G). Given a positive integer k and a graph G, the DISJUNCTIVE DOMINATION DECISION PROBLEM (DDDP) is to decide whether G has a disjunctive dominating set of cardinality at most k. In this article, we first propose a polynomial time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a (ln(Delta 2 + Delta + 2) + 1)-approximation algorithm for MDDP, where Delta is the maximum degree of input graph G = (V, E) and prove that MDDP can not be approximated within (1 - epsilon) ln(vertical bar V vertical bar) for any epsilon > 0 unless NP subset of DTIME(vertical bar V vertical bar(O (log log vertical bar V vertical bar))). Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree 3.

关键词： Domination Chordal graph graph algorithm Approximation algorithm Np-complete Apx-complete

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Maximizing Influence of Leaders in Social Networks 21

Maximizing Influence of Leaders in Social Networks

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27th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD)

作者： Zhou, Xiaotian Zhang, Zhongzhi Fudan Univ Shanghai Key Lab Intelligent Informat Proc Shanghai 200433 Peoples R China Fudan Univ Sch Comp Sci Shanghai 200433 Peoples R China Fudan Univ Shanghai Blockchain Engn Res Ctr Res Inst Intelligent Complex Syst Shanghai 200433 Peoples R China

ISBN: (纸本)9781450383325

The operation of adding edges has been frequently used to the study of opinion dynamics in social networks for various purposes. In this paper, we consider the edge addition problem for the DeGroot model of opinion dynamics in a social network with n nodes and m edges, in the presence of a small number s << n of competing leaders with binary opposing opinions 0 or 1. Concretely, we pose and investigate the problem of maximizing the equilibrium overall opinion by creating k new edges in a candidate edge set, where each edge is incident to a 1-valued leader and a follower node. We show that the objective function is monotone and submodular. We then propose a simple greedy algorithm with an approximation factor (1 - 1/e) that approximately solves the problem in O(n(3)) time. Moreover, we provide a fast algorithm with a (1 - 1/e - epsilon) approximation ratio and (O) over tilde (mk epsilon(-2)) time complexity for any epsilon > 0, where (O) over tilde(center dot) notation suppresses the poly(log n) factors. Extensive experiments demonstrate that our second approximate algorithm is efficient and effective, which scales to large networks with more than a million nodes.

关键词： Opinion dynamics social network multi-agent system graph algorithm influence maximization discrete optimization Laplacian solver

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Induced Matching in Some Subclasses of Bipartite graphs 3rd

Induced Matching in Some Subclasses of Bipartite Graphs

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3rd International Conference on algorithms and Discrete Applied Mathematics (CALDAM)

作者： Pandey, Arti Panda, B. S. Dane, Piyush Kashyap, Manav Indian Inst Technol Ropar Dept Math Nangal Rd Rupnagar 140001 Punjab India Indian Inst Technol Delhi Dept Math Hauz Khas New Delhi 110016 India

ISBN: (纸本)9783319530062;9783319530079

For a graph G = (V, E), a set M subset of E is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching in G if G[ M], the subgraph of G induced by M, is same as G[ S], the subgraph of G induced by S = {v is an element of V | v is incident on an edge of M}. The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Induced Matching Decision problem is NP-complete on bipartite graphs, but polynomial time solvable for convex bipartite graphs. In this paper, we show that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs and perfect elimination bipartite graphs. On the positive side, we propose polynomial time algorithms to solve the Maximum Induced Matching problem in circularconvex bipartite graphs and triad-convex bipartite graphs by making polynomial reductions from the Maximum Induced Matching problem in these graph classes to the Maximum Induced Matching problem in convex bipartite graphs.

关键词： Matching Induced matching Bipartite graphs graph algorithm NP-complete

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DLQ: A System for Label-Constrained Reachability Queries on Dynamic graphs 21

DLQ: A System for Label-Constrained Reachability Queries on ...

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30th ACM International Conference on Information and Knowledge Management (CIKM)

作者： Peng, You Zhao, Wenjie Zhang, Wenjie Lin, Xuemin Zhang, Ying Univ New South Wale Sydney Australia

ISBN: (纸本)9781450384469

Label-Constraint Reachability query (LCR) which extracts of reachability information from large edge-labeled graphs, has attracted tremendous interest. Various LCR algorithms have been proposed to solve this fundamental query, which has a wide range of applications in social networks, biological networks, economic networks, etc. In this paper, we implement the state-of-the-art P2H+ algorithm as well as functions to analyze the effectiveness. Moreover, our Dynamic LCR Query (DLQ) system also supports dynamic updates with the 2-hop labeling method. In this demonstration, we present the DLQ system for Label-Constrained Reachability Queries that utilize the 2-hop labeling algorithm with dynamic graph maintenance.

关键词： graph database label constrained reachability graph algorithm dynamic graph

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Complexity of the Packing Coloring Problem for Trees

Complexity of the Packing Coloring Problem for Trees

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34th International Workshop on graph-Theoretic Concepts in Computer Science

作者： Fiala, Jiri Golovach, Petr A. Charles Univ Prague Dept Appl Math CR-11800 Prague Czech Republic Univ Bergen Dept Informat N-5020 Bergen Norway

ISBN: (纸本)9783540922476

Packing coloring is a partitioning of the vertex set of a graph with the property that vertices in the i-th class have pairwise distance greater than i. We solve an open problem of Goddard et al. and show that the decision whether a tree allows a packing coloring with at most k classes is NP-complete. We accompany this NP-hardness result by a polynomial time algorithm for trees for closely related variant of the packing coloring problem where the lower bounds on the distances between vertices inside color classes are determined by an infinite nondecreasing sequence of bounded integers.

关键词： Packing coloring computational complexity graph algorithm chordal graph

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Identify the centerline of tubular structure in medical images

Identify the centerline of tubular structure in medical imag...

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Medical Imaging 2005 Conference

作者： Ching, YT Yeh, C Natl Chiao Tung Univ Dept Comp & Informat Sci Hsinchu 30050 Taiwan

ISBN: (纸本)0819457213

Finding the centerline of the tubular structure helps to segment or analyze the organs such as the vessels or neuron fibers in medical images. This paper described a semi-automatic method using the minimum cost path finding and Hessian matrix analysis in scale space to calculate the centerline of tubular structure organs. Unlike previous approaches, exhaustive search for tine-like shapes in every scale is prevent. Centerline pixels candidates and the width of the vessel are extracted by analyzing the intensity profile along the gradient vectors in the image. A verification procedure using Hassian matrix analysis with the scale obtained from the gradient analysis is applied to those candidates. Results obtained from the Hessian matrix analysis are used to construct a weighted graph. Finding the minimum cost path in the graph gives the centerline of the tubular structure. The method is applied to find the centerline of the vessels in the 2D angiogram and the neuron fibers in the 3D confocal microscopic images.

关键词： Hessian matrix analysis centerline graph algorithm angiogram confocal microscopic image

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