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We consider the following clustering problems: given a general undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone… (More)

We present a general technique for detecting and counting small subgraphs. It consists of forming special linear combinations of the numbers of occurrences of different induced subgraphs of fixed size in a graph. These combinations can be efficiently computed by rectangular matrix multiplication. Our two main results utilizing the technique are as follows.… (More)

We present a general technique for detecting and counting small subgraphs. It consists in forming special linear combinations of the numbers of occurrences of different induced subgraphs of fixed size in a graph. The combinations can be efficiently computed by rectangular matrix multiplication.
Our two main results utilizing the technique are as follows.… (More)

For a set of rooted, unordered, distinctly leaf-labeled trees, the NP-hard maximum agreement subtree problem (MAST) asks for a tree contained (up to isomorphism or homeomorphism) in all of the input trees with as many labeled leaves as possible. We study the ordered variants of MAST where the trees are uniformly or non-uniformly ordered. We provide the… (More)

The maximum rooted resolved triplets consistency problem takes as input a set R of resolved triplets and asks for a rooted phylo-genetic tree that is consistent with the maximum number of elements in R. This paper studies the polynomial-time approximability of a generalization of the problem where in addition to resolved triplets, the input may contain fan… (More)