Artificial immune systems (AIS) are algorithms that are based on the structure and mechanisms of the vertebrate immune system. Clonal selection is a process that allows lymphocytes to launch a quick response to known pathogens and to adapt to new, previously unencountered ones. This paper presents a parallel island model algorithm based on the clonal selection principles for solving the Graph Coloring Problem. The performance of the algorithm over a set of well-established benchmark graphs and random graphs is compared with a parallel Tabu Search algorithm.

The problem of diagnostic test scheduling (DTS) is to assign to each edge e of a diagnostic graph G a time interval of length l(e) so that intervals corresponding to edges at any given vertex do not overlap and the overall finishing time is minimum. In this correspondence we show that the DTS problem is NP-complete. Then we present a longest, first sequential scheduling algorithm which runs in worst case time O(dm log n) and uses O(m) space to produce a solution of length less than four times optimal. Then we show that the general performance bound can be strengthened to 3 * OPT(G) for low-degree graphs and to 2 ·OPT(G) in some special cases of binomial diagnostic graphs.

A counterexample is given to show the partial correctness of a matrix decomposition algorithm proposed by Ramanujam in 1973. It is pointed out that the edge coloring approach results in the most efficient algorithms for the decomposition problem.