Abstract. We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network analysis, an important area in bioinformatics. We give two positive results and three negative results that together draw sharp borderlines between tractable and intractable instances of the problem. 1

We propose an effective polynomial-time preprocessing strategy for intractable median problems. Developing a new methodological framework, we show that if the input instances of generally intractable problems exhibit a sufficiently high degree of similarity between each other on average, then there are efficient exact solving algorithms. In other words, we show that the median problems Swap Median Permutation, Consensus Clustering, Kemeny Score, and Kemeny Tie Score all are fixed-parameter tractable with respect to the parameter “average distance between input objects”. To this end, we develop the new concept of “partial kernelization” and identify interesting polynomial-time solvable special cases for the considered problems.

Abstract. In this paper, we study the pattern matching problem in given intervals. Depending on whether the intervals are given a priori for pre-processing, or during the query along with the pattern or, even in both cases, we develop solutions for different variants of this problem. In particular, we present efficient indexing schemes for each of the above variants of the problem. 1

Abstract. This paper deals with the Circular Pattern Matching Problem (CPM). In CPM, we are interested in pattern matching between the text T and the circular pattern C(P) of a given pattern P = P1... Pm. The circular pattern C(P) is formed by concatenating P1 to the right of Pm. We can view C(P) as a set of m patterns starting at positions j ∈ [1..m] and wrapping around the end and if any of these patterns matches T, we find a match for C(P). In this paper, we present two efficient data structures to index circular patterns. This problem has applications in pattern matching in geometric and astronomical data as well as in computer graphics and bioinformatics. 1

Abstract. In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the SORTING BY TRANSPOSITIONS problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the SORTING BY TRANSPOSITIONS problem is NP-hard. As a corollary of our result, we also prove that the following problem from [9] is NP-hard: given a permutation π, is it possible to sort π using db(π)/3 permutations, where db(π) is the number of breakpoints of π?