Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

Hardness of r-dominating set on graphs of diameter (r + 1)

Abstract. The dominating set problem has been extensively studied in the realm of parameterized complexity. It is one of the most common sources of reductions while proving the parameterized intractability of problems. In this paper, we look at dominating set and its generalization r-dominating set on graphs of bounded diameter in the realm of parameterized complexity. We show that Dominating set remains W[2]-hard on graphs of diameter 2, while r-dominating set remains W[2]-hard on graphs of diameter r +1. The lower bound on the diameter in our intractability results is the best possible, as r-dominating set is clearly polynomial time solvable on graphs of diameter at most r.

Variations in Tetrodotoxin Levels in Populations of Taricha granulosa are Expressed in the Morphology of Their Cutaneous Glands

Tetrodotoxin (TTX), one of the most toxic substances in nature, is present in bacteria, invertebrates, fishes, and amphibians. Marine organisms seem to bioaccumulate TTX from their food or acquire it from symbiotic bacteria, but its origin in amphibians is unclear. Taricha granulosa can exhibit high TTX levels, presumably concentrated in skin poison glands, acting as an agent of selection upon predatory garter snakes (Thamnophis). This co-evolutionary arms race induces variation in T. granulosa TTX levels, from very high to undetectable. Using morphology and biochemistry, we investigated differences in toxin localization and quality between two populations at the extremes of toxicity. TTX concentration within poison glands is related to the volume of a single cell type in which TTX occurs exclusively in distinctive secretory granules, suggesting a relationship between granule structure and chemical composition. TTX was detected in mucous glands in both populations, contradicting the general understanding that these glands do not secrete defensive chemicals and expanding currently held interpretations of amphibian skin gland functionality. Skin secretions of the two populations differed in low-mass molecules and proteins. Our results demonstrate that interpopulation variation in TTX levels is related to poison gland morphology

Binary Jumbled Pattern Matching on Trees and Tree-Like Structures

Abstract. Binary jumbled pattern matching asks to preprocess a binary string S in order to answer queries (i, j) which ask for a substring of S that is of length i and has exactly j 1-bits. This prob-lem naturally generalizes to vertex-labeled trees and graphs by replacing “substring ” with “connected subgraph”. In this paper, we give an O(n2 / log2 n)-time solution for trees, matching the currently best bound for (the simpler problem of) strings. We also give an O(g2/3n4/3/(logn)4/3)-time solution for strings that are compressed by a grammar of size g. This solution improves the known bounds when the string is compressible under many popular compression schemes. Finally, we prove that the problem is fixed-parameter tractable with respect to the treewidth w of the graph, even for a constant number of different vertex-labels, thus improving the previous best nO(w) algorithm [ICALP’07].