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BACKGROUND Recent biological discoveries have shown that clustering large datasets is essential for better understanding biology in many areas. Spectral clustering in particular has proven to be a powerful tool amenable for many applications. However, it cannot be directly applied to large datasets due to time and memory limitations. To address this issue,(More)
Mitchell and Ternovska [49, 50] propose a constraint programming framework for search problems that is based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX). In this framework, the problem is encoded in a logic, an instance of the problem is represented by a finite structure, and(More)
We study the problem of designing fault tolerant routings in both complete and complete bipartite optical networks. We show that this problem has strong connections to various fundamental problems in design theory. Using a design theory approach, we find optimal f-fault tolerant arc-forwarding indexes for all complete networks and all complete balanced(More)
For digraphs G and H, a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f (u)f (v) ∈ A(H). If moreover each vertex u ∈ V (G) is associated with costs c i (u), i ∈ V (H), then the cost of a homomorphism f is u∈V (G) c f (u) (u). For each fixed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), is the(More)
We present sequential and parallel algorithms for various embedding problems on bounded degree partial k-trees and k-connected partial k-treess these include subgraph isomorphism and topological embedding, known to be NP-complete for general partial k-trees. As well as contributing to our understanding of the types of graphs for which these problems are(More)