We show that, for any n-vertex graph G and integer parameter k,there |I|#k,and that all such sets can be listed in time ). These bounds are tight when n/4 n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3+3 /4) 2.4150 , improving a previous algorithm of Lawler (1976).

We describe the summary graph lattice for dataflow analysis of programs that dynamically construct XML documents. Summary graphs have successfully been used to provide static guarantees in the JWIG language for programming interactive Web services. In particular, the JWIG compiler is able to check validity of dynamically generated XHTML documents and to type check dynamic form data. In this paper we present summary graphs and indicate their applicability for various scenarios. We also show that the expressive power of summary graphs is similar to that of the regular expression types from XDuce, but that the extra structure in summary graphs makes them more suitable for certain program analyses.

Abstract: The efficient enumeration of maximal cliques has applications in microarray analysis and a number of other foundational problems of computational biology. In this paper, we analyze and test existing maximal clique enumeration algorithms for various classes of graphs. The classic branch and bound algorithm of Bron and Kerbosch proves to be relatively fast for sparse graphs, but slows considerably as edge density increases. Attempts to improve this algorithm are discussed. Experimental results demonstrate the difficulty of making improvements, especially when analyzing the overlap between cliques. Novel strategies for maximal clique enumeration algorithms are also described and placed in the context of ongoing research.

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This is the second annual progress report for the ALCOM-FT project, supported by the European