6,531 research outputs found
Maximum common subgraph isomorphism algorithms for the matching of chemical structures
The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks
Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six
We consider the problem of counting all k-vertex subgraphs in an input graph, for any constant k. This problem (denoted SUB-CNT_k) has been studied extensively in both theory and practice. In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time algorithms for clique and 4-cycle counting for bounded degeneracy graphs. This is a rich class of sparse graphs that contains, for example, all minor-free families and preferential attachment graphs. The techniques from this result have inspired a number of recent practical algorithms for SUB-CNT_k. Towards a better understanding of the limits of these techniques, we ask: for what values of k can SUB_CNT_k be solved in linear time?
We discover a chasm at k=6. Specifically, we prove that for k < 6, SUB_CNT_k can be solved in linear time. Assuming a standard conjecture in fine-grained complexity, we prove that for all k ? 6, SUB-CNT_k cannot be solved even in near-linear time
Topological network alignment uncovers biological function and phylogeny
Sequence comparison and alignment has had an enormous impact on our
understanding of evolution, biology, and disease. Comparison and alignment of
biological networks will likely have a similar impact. Existing network
alignments use information external to the networks, such as sequence, because
no good algorithm for purely topological alignment has yet been devised. In
this paper, we present a novel algorithm based solely on network topology, that
can be used to align any two networks. We apply it to biological networks to
produce by far the most complete topological alignments of biological networks
to date. We demonstrate that both species phylogeny and detailed biological
function of individual proteins can be extracted from our alignments.
Topology-based alignments have the potential to provide a completely new,
independent source of phylogenetic information. Our alignment of the
protein-protein interaction networks of two very different species--yeast and
human--indicate that even distant species share a surprising amount of network
topology with each other, suggesting broad similarities in internal cellular
wiring across all life on Earth.Comment: Algorithm explained in more details. Additional analysis adde
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