© DIGITAL VISION [Sparse graph codes and message-passing algorithms for binning and coding with side information]

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

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

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 non-negative reals, although

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 cell-probe model. This lower bound holds even for sparse (polylog(n)-degree) graphs, and it is not an “incompressibility ” bound: we prove a

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

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

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

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

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 clique-width. Fouquet and