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119
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 76 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Linear Assignment Problems and Extensions
"... This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems ..."
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Cited by 45 (0 self)
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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial threedimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published
An Emulator Network for
 SIMD Machine Interconnection Networks, in: Proc. 6 th annual symposium on Computer architecture
, 1979
"... Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is ..."
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Cited by 39 (4 self)
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Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is colored according to community membership, which was determined using a leadingeigenvector spectral method followed by KernighanLin nodeswapping steps [64, 86, 107]. To determine community placement, we used the FruchtermanReingold graph visualization [45], a forcedirected layout method that is related to maximizing a quality function known as modularity [92]. To apply this method, we treated the communities as if they were themselves the nodes of a (significantly smaller) network with connections rescaled by intercommunity links. We then used the KamadaKawaii springembedding graph visualization algorithm [62] to place the nodes of each individual community (ignoring intercommunity links) and then to rotate and flip the communities for optimal placement (including intercommunity links). We gratefully acknowledge Amanda Traud for preparing this figure. COMMUNITIES IN NETWORKS
Selected Topics on Assignment Problems
, 1999
"... We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and co ..."
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Cited by 26 (1 self)
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We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and communication assignment problems.
Edgecut bounds on network coding rates
 J. Network and Systems Management
, 2006
"... AbstractActive networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A ne ..."
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Cited by 26 (3 self)
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AbstractActive networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bitwise XOR, of selected received packets. The bound generalizes an edgecut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened dseparation conditions are satised. The bound improves on the cutset bound and its efcacy is demonstrated by showing that routing is rateoptimal for some commonly cited examples in the networking literature. Index Terms Network capacity, network coding, active networks, dseparation 1.
Convex and network flow optimization for structured sparsity
 JMLR
"... We consider a class of learning problems regularized by a structured sparsityinducing norm defined as the sum of ℓ2 or ℓ∞norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address ..."
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Cited by 16 (6 self)
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We consider a class of learning problems regularized by a structured sparsityinducing norm defined as the sum of ℓ2 or ℓ∞norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of ℓ∞norms can be computed exactly in polynomial time by solving a quadratic mincost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with nonoverlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multitask learning of treestructured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.
Combinatorial algorithms for wireless information flow
 IN SODA ’09: PROCEEDINGS OF THE TWENTIETH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2009
"... A longstanding open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among t ..."
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Cited by 16 (3 self)
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A longstanding open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse proposed a linear binary deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the mincut maxflow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the binary adjacency matrices describing sourcedestination cuts. However, since there exists an exponential number of cuts, identifying the capacity through exhaustive search becomes infeasible. In this paper, we develop a polynomial time algorithm that discovers the relay encoding strategy to achieve the mincut value in binary linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between edges to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple onebit processing at the intermediate nodes, thereby constructively yielding finite length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.
The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density
 SOCIOLOGICAL METHODOLOGY
, 2001
"... This study shows various ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of ..."
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Cited by 16 (3 self)
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This study shows various ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of independent paths that connect every pair of nodes in the network, the higher the social cohesion. The cohesiveness of a group is also measured by the extent to which it is not disconnected by removal of 1, 2, 3,..., n actors. Menger's Theorem proves that these two measures are equivalent. Within this graph theoretic framework, we evaluate the family of concepts of cohesion and establish the validity of a pair of related measures: 1. Connectivity  the minimum number k of its actors whose removal would not allow the group to remain connected or would reduce the group to but a single member  measures the social cohesion of a group at a general level. 2. Conditional density measures cohesion on a finer scale as a proportion of ties beyond that required by a graph's connectivity k over the number of ties that would force it to k + 1. Calibrated for successive values of k, these two measures combine into an aggregate measure of social cohesion, suitable for both smalland largescale network studies. Using these measures to define the core of a new methodology of cohesive blocking, we offer hypotheses about the consequences of cohesive blocks for social groups and their members, and explore empirical examples that illustrate the significance, theoretical relevance, and predictiveness of cohesive blocking in a variety of substantively important applications in sociology.
A SelfStabilizing Algorithm For The Maximum Flow Problem
 Distributed Computing
, 1995
"... . The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents the first distribute ..."
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Cited by 14 (2 self)
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. The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents the first distributed selfstabilizing algorithm for the maximum flow problem. Starting from an arbitrary state, the algorithm computes the maximum flow in a acyclic network in finitely many steps. Since the algorithm is selfstabilizing, it is inherently tolerant to transient faults and can automatically adjust to topology changes and to changes in other parameters of the problem. The paper presents extensive experimental results to indicate that the algorithm requires n 2 moves in an averagecase setting. A slight modification of the original algorithm is also presented and it is conjectured that the new algorithm computes a maximum flow in arbitrary networks. Key words. distributed algorithms, faulttoler...