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Sparse Graph Codes for Side
"... © DIGITAL VISION [Sparse graph codes and messagepassing algorithms for binning and coding with side information] ..."
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© DIGITAL VISION [Sparse graph codes and messagepassing algorithms for binning and coding with side information]
Graded sparse graphs and matroids
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 2007
"... Sparse graphs and their associated matroids [Whiteley, 1988; Whiteley, 1996; Lee and Streinu, 2007; Streinu and Theran, 2007] play an important role in rigidity theory, where they capture the combinatorics of generically rigid structures [Laman, 1970; Tay, 1984]. We define a new family called grade ..."
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Cited by 8 (6 self)
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Sparse graphs and their associated matroids [Whiteley, 1988; Whiteley, 1996; Lee and Streinu, 2007; Streinu and Theran, 2007] play an important role in rigidity theory, where they capture the combinatorics of generically rigid structures [Laman, 1970; Tay, 1984]. We define a new family called
Dynamic Representations of Sparse Graphs
 In Proc. 6th International Workshop on Algorithms and Data Structures (WADS
, 1999
"... We present a linear space data structure for maintaining graphs with bounded arboricity  a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth  under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in wors ..."
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Cited by 14 (0 self)
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We present a linear space data structure for maintaining graphs with bounded arboricity  a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth  under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries
Girth of Sparse Graphs
 2002), 194  200. ILWOO CHO
"... Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with Θ(n) edges. Roughly speaking, there is one model for each kernel, i.e., each symmetric measurable function from [0,1] 2 to the nonnegative reals, although the d ..."
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Cited by 78 (6 self)
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Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with Θ(n) edges. Roughly speaking, there is one model for each kernel, i.e., each symmetric measurable function from [0,1] 2 to the nonnegative reals, although
Distance oracles for sparse graphs
 IN PROCEEDINGS OF THE 50TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
"... Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efficient algorithm to construct an approximate distance oracle using space O(kn 1+1/k) that can answer queries i ..."
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Cited by 26 (4 self)
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of the graph. Naturally, the following question arises: what happens for sparse graphs? In this paper we give a new lower bound for approximate distance oracles in the cellprobe model. This lower bound holds even for sparse (polylog(n)degree) graphs, and it is not an “incompressibility ” bound: we prove a
Hamiltonian Cycles in Sparse Graphs
, 2004
"... The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle within a graph is a simple cycle that pas ..."
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Cited by 1 (1 self)
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that passes through each vertex exactly once. This thesis provides a history of the problem, a survey of major results, as well as a detailed account of the author’s original contributions with respect to sparse graphs. The first of these is the “Stonecarver’s Algorithm”, which is successful in finding
Linear Choosability of Sparse Graphs
, 2010
"... We study the linear list chromatic number, denoted lc`(G), of sparse graphs. The maximum average degree of a graph G, denoted mad(G), is the maximum of the average degrees of all subgraphs of G. It is clear that any graph G with maximum degree ∆(G) satisfies lc`(G) ≥ d∆(G)/2e+1. In this paper, we pr ..."
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We study the linear list chromatic number, denoted lc`(G), of sparse graphs. The maximum average degree of a graph G, denoted mad(G), is the maximum of the average degrees of all subgraphs of G. It is clear that any graph G with maximum degree ∆(G) satisfies lc`(G) ≥ d∆(G)/2e+1. In this paper, we
Resource allocation on sparse graphs
"... Optimal resource allocation is a well known problem in the area of distributed computing [1, 2] to which significant effort has been dedicated within the computer science community. The problem itself is quite general and is applicable to other areas as well where a large number of nodes are require ..."
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from some arbitrary distribution. The nodes are located on a randomly chosen sparse graph of some connectivity. The goal is to migrate tasks on the graph such that demands will be satisfied while minimising the migration of (sub)tasks. Decisions on messages to be passed are carried out locally. We
The diameter of random sparse graphs
, 2000
"... We consider the diameter of a random graph G(n, p) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of ..."
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Cited by 40 (6 self)
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We consider the diameter of a random graph G(n, p) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter
On Variations of P_4Sparse Graphs
, 2002
"... Hoang defined the P 4 sparse graphs as the graphs where every set of five vertices induces at most one P 4 . These graphs attracted considerable attention in connection with the P 4 structure of graphs and the fact that P 4 sparse graphs have bounded cliquewidth. Fouquet and ..."
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Cited by 5 (1 self)
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Hoang defined the P 4 sparse graphs as the graphs where every set of five vertices induces at most one P 4 . These graphs attracted considerable attention in connection with the P 4 structure of graphs and the fact that P 4 sparse graphs have bounded cliquewidth. Fouquet and
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