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19
Information Theory and Communication Networks: An Unconsummated Union
 IEEE Trans. Inform. Theory
, 1998
"... Information theory has not yet had a direct impact on networking, although there are similarities in concepts and methodologies that have consistently attracted the attention of researchers from both fields. In this paper, we review several topics that are related to communication networks and that ..."
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Cited by 133 (5 self)
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Information theory has not yet had a direct impact on networking, although there are similarities in concepts and methodologies that have consistently attracted the attention of researchers from both fields. In this paper, we review several topics that are related to communication networks and that have an information theoretic flavor, including multiaccess protocols, timing channels, effective bandwidth of bursty data sources, deterministic constraints on datastreams, queueing theory, and switching networks. Keywords Communication networks, multiaccess, effective bandwidth, switching I. INTRODUCTION Information theory is the conscience of the theory of communication; it has defined the "playing field" within which communication systems can be studied and understood. It has provided the spawning grounds for the fields of coding, compression, encryption, detection, and modulation and it has enabled the design and evaluation of systems whose performance is pushing the limits of wha...
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 51 (8 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
A simple algorithm for finding maximal network flows and an application to the Hitchcock problem
 CANADIAN JOURNAL OF MATHEMATICS
, 1957
"... ..."
A Fast and Simple Algorithm for the Maximum Flow Problem
 OPERATIONS RESEARCH
, 1989
"... We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best b ..."
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Cited by 32 (6 self)
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We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best bound of O(nm log(n 2 /m)), obtained by Goldberg and Taran, by a factor of log n for networks that are both nonsparse and nondense without using any complex data structures. We also describe a parallel implementation of the algorithm that runs in O(n'log U log p) time in the PRAM model with EREW and uses only p processors where p = [m/n
EdgeCut Bounds On Network Coding Rates
 Journal of Network and Systems Management
, 2006
"... Abstract — Two bounds on network coding rates are reviewed that generalize edgecut bounds on routing rates. The simpler bound is a bidirected cutset bound which generalizes and improves upon a flow cutset bound that is standard in networking. It follows that routing is rateoptimal if routing ach ..."
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Cited by 24 (2 self)
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Abstract — Two bounds on network coding rates are reviewed that generalize edgecut bounds on routing rates. The simpler bound is a bidirected cutset bound which generalizes and improves upon a flow cutset bound that is standard in networking. It follows that routing is rateoptimal if routing achieves the standard flow cutset bound. The second bound improves on the cutset bound, and it involves progressively removing edges from a network graph and checking whether certain strengthened dseparation conditions are satisfied. I.
Fully Dynamic Planarity Testing with Applications
"... The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without ..."
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Cited by 6 (0 self)
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The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without violating planarity. We show how to support each of the above operations in O(n2=3) time, where n is the number of vertices in the graph. The bound for tests and deletions is worstcase, while the bound for insertions is amortized. This is the first algorithm for this problem with sublinear running time, and it affirmatively answers a question posed in [11]. The same data structure has further applications in maintaining the biconnected and triconnected components of a dynamic planar graph. The time bounds are the same: O(n2=3) worstcase time per edge deletion, O(n2=3) amortized time per edge insertion, and O(n2=3) worstcase time to check whether two vertices are either biconnected or triconnected.
Maximum Flows and Parametric Shortest Paths in Planar Graphs
"... We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously ..."
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Cited by 6 (1 self)
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We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once. The resulting maximumflow algorithm is identical to the recent algorithm of Borradaile and Klein [J. ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change Ω(n²) times in the worst case, suggesting that a different method may be required to efficiently compute maximum flows in highergenus graphs.
SeparatorBased Sparsification II: Edge And Vertex Connectivity
 SIAM J. Comput
, 1998
"... . We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2 and 3vertexconnectivity, and 3 and 4edgeconnec ..."
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Cited by 3 (0 self)
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. We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2 and 3vertexconnectivity, and 3 and 4edgeconnectivity in a planar graph in O(n 1/2 ) amortized time per insertion, deletion, or connectivity query. All of the data structures handle insertions that keep the graph planar without regard to any particular embedding of the graph. Our algorithms are based on a new type of sparsification combined with several properties of separators in planar graphs. Key words. analysis of algorithms, dynamic data structures, edge connectivity, vertex connectivity, planar graphs AMS subject classifications. 68P05, 68Q20, 68R10 PII. S0097539794269072 1. Introduction. Sparse certificates, small graphs that retain some property of a larger graph, appear often in graph theory, especially in problems of edge and...
The multicast capacity of acyclic, deterministic relay networks with no interference
, 2005
"... The multicast capacity is determined for acyclic networks that have deterministic links with broadcasting at the transmitters and no interference at the receivers. Such networks were studied by M. R. Aref, and are here called Aref networks. The multicast capacity is shown to have a maxflow, mincu ..."
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Cited by 3 (1 self)
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The multicast capacity is determined for acyclic networks that have deterministic links with broadcasting at the transmitters and no interference at the receivers. Such networks were studied by M. R. Aref, and are here called Aref networks. The multicast capacity is shown to have a maxflow, mincut interpretation. This result complements existing theory for networks of directed channels, networks of undirected channels, and packet erasure networks. It is also shown that one cannot always separate channel and network coding in Aref networks.