A compact labeling scheme for series-parallel graphs

Compact Labeling Scheme for Ancestor Queries

We consider the following problem. Given a rooted tree T , label the nodes of T in the most compact way such that given the labels of two nodes u and v one can determine in constant time, by looking only at the labels, if u is ancestor of v. The best known labeling scheme is rather straightforward and uses labels of length at most 2 log2 n bits each, where n is the number of nodes in the tree. ...

Improved Compact Routing Scheme for Chordal Graphs

Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs

In this paper, we propose a new compact and low delay routing labeling scheme for Unit Disk Graphs (UDGs) which often model wireless ad hoc networks. We show that one can assign each vertex of an n-vertex UDG G a compact O(log n)-bit label such that, given the label of a source vertex and the label of a destination, it is possible to compute efficiently, based solely on these two labels, a neig...

Parallel Algorithms for Series Parallel Graphs

In this paper, a parallel algorithm is given that, given a graph G = (V;E), decides whether G is a series parallel graph, and if so, builds a decomposition tree for G of series and parallel composition rules. The algorithm uses O(log jEj log jEj) time and O(jEj) operations on an EREW PRAM, and O(log jEj) time and O(jEj) operations on a CRCW PRAM (note that ifG is a simple series parallel graph,...

A fuzzy reliability model for series-parallel systems

Fuzzy set based methods have been proved to be effective in handling many types of uncertainties in different fields, including reliability engineering. This paper presents a new approach on fuzzy reliability, based on the use of beta type distribution as membership function. Considering experts' ideas and by asking operators linguistic variables, a rule base is designed to determine the level ...