Efficient computation of implicit representations of sparse graphs

Efficient Computation of Implicit Representations of Sparse Graphs

The problem of nding an implicit representation for a graph such that vertex ad-jacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show here how to construct such a representation eeciently by providing simple and optimal algorithms, bo...

Eecient Computation of Implicit Representations of Sparse Graphs (revised Version) Eecient C O M Putation of Implicit Representations of Sparse Graphs

The problem of nding an implicit representation for a graph such that vertex ad jacency can be tested quickly is fundamental to all graph algorithms In particular it is possible to represent sparse graphs on n vertices using O n space such that vertex adjacency is tested in O time We show here how to construct such a representation e ciently by providing simple and optimal algorithms both in a ...

E cient Computation of Compact Representations of Sparse Graphs

Sparse graphs e g trees planar graphs relative neighborhood graphs are among the commonly used data structures in computational geometry The problem of nding a compact representation for sparse graphs such that vertex adjacency can be tested quickly is fundamental to several geometric and graph algorithms We provide here simple and optimal algorithms for constructing a compact representation of...

Dynami Representations of Sparse Graphs ?

Efficient computation of sparse structures

Basic graph structures such as maximal independent sets (MIS’s) have spurred much theoretical research in randomized and distributed algorithms, and have several applications in networking and distributed computing as well. However, the extant (distributed) algorithms for these problems do not necessarily guarantee fault-tolerance or load-balance properties. We propose and study “lowaverage deg...