DCR-2002, 16 July, Bologna Outline: • Motivation: real-time coordination of sensors in a high-latency network • Modeling coordination as graph colouring • Soft graph colouring for real-time responsiveness • A class of distributed anytime algorithms (synchronous) • Convergence • Tightness of constraints: conservative variant • Scalability and robustness • Asynchronous execution • Very high commu...

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.

P systems have been known to provide efficient polynomial (often linear) deterministic solutions hard problems. In particular, cP shown very crisp and such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., solves SAT in square-root-sublinear time, this paper proposes an orders-of-magnitude-faster solution, running logarithmic using fi...

For k ≥ 2 we define a class of graphs Hk = {G : every block of G has at most k vertices}. The class Hk contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from Hk.

Perfect colouring of isonemal fabrics by thin striping of warp and weft with more than two colours is examined. Examples of thin striping in all possible species with no redundancy and with redundant cells arranged as twills are given. Colouring woven flat tori is discussed.

Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which descisions are made locally with no information about the graph’s global structure is particuarly challenging. In this article we analyse the complexity of a decentralised colouring algorithm that has recently been proposed for channel selection in wireless computer networks.

In this paper, we investigate the problem of graph list colouring in the on-line setting. We provide several results on paintability of graphs in the model introduced by Schauz [13] and Zhu [19]. We prove that the on-line version of Ohba’s conjecture is true in the class of planar graphs. We also consider several alternate on-line list colouring models.