Learn More
In this paper we consider the approximability of the maximum induced matching problem. We prove that there is some xed constant c such that the problem of approximating a maximum induced matching in 3s-regular graphs within a factor of c is NP-hard, for each s 1. In addition we give an approximation algorithm with asymptotic performance ratio d ? 1 for the(More)
The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to(More)
In this paper we consider the problem of finding large collections of vertices and edges satisfying particular separation properties in random regular graphs of degree r, for each fixed r ≥ 3. We prove both constructive lower bounds and combinatorial upper bounds on the maximal sizes of these sets. The lower bounds are proved by analysing a class of(More)
Graph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplicates) and (ii) how best to process the generated candidate(More)
A graph-based approach to document classification is described in this paper. The graph representation offers the advantage that it allows for a much more expressive document encoding than the more standard bag of words/phrases approach , and consequently gives an improved classification accuracy. Document sets are represented as graph sets to which a(More)
In this paper we study the size of generalised dominating sets in two graph processes that are widely used to model aspects of the World Wide Web. On the one hand, we show that graphs generated this way have fairly large dominating sets (i.e., linear in the size of the graph). On the other hand, we present efficient strategies to construct small dominating(More)
Frequent sub-graph mining entails two significant overheads. The first is concerned with candidate set generation. The second with isomorphism checking. These are also issues with respect to other forms of frequent pattern mining but are exacerbated in the context of frequent sub-graph mining. To reduced the search space, and address these twin overheads, a(More)