In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial optimization problem has applications in computational biology and is NP-hard. Many different heuristic and exact methods exist for this problem, such as a Greedy approach, Ant Colony Optimization, or Integer Linear Programming. In this paper, we formulate the MCSP as a Dynamic Program and develop an exact solution algorithm based on Decision Diagrams for it. We also introduce a restricted Decision Diagram that allows to compute heuristic solutions to the MCSP and compare the quality of solution and runtime on instances from literature with existing approaches. Our approach scales well and is suitable for heuristic solution of large-scale instances.

In this paper we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists. Given a truth table representation of a Boolean function f the switch-list representation (SLR) of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include the language SL of all SLR in the Knowledge Compilation Map [Darwiche and Marquis, 2002] and to argue, that SL may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First we compare SL with a number of standard representation languages (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis we also give a short proof of a long standing open question from [Darwiche and Marquis, 2002], namely the incomparability of MODS (models) and PI (prime implicates) languages. Next we analyze which standard transformations and queries (those considered in [Darwiche and Marquis, 2002] can be performed in poly-time with respect to the size of the input SLR. We show that this collection is quite broad and the combination of poly-time transformations and queries is quite unique.

In this paper, we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists, which are closely related to interval representations. Given a truth table representation of a Boolean function f the switch-list representation of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include this type of representation in the Knowledge Compilation Map by Darwiche and Marquis and to argue that switch-lists may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First, we compare switch-list representations with a number of standard representations (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis, we also give a short proof of a longstanding open question proposed by Darwiche and Marquis, namely the incomparability of MODS (models) and PI (prime implicates) representations. Next, using the succinctness result between switch-lists and OBDDs, we develop a polynomial time compilation algorithm from switch-lists to OBDDs. Finally, we analyze which standard transformations and queries (those considered by Darwiche and Marquis) can be performed in polynomial time with respect to the size of the input if the input knowledge is represented by a switch-list. We show that this collection is very broad and the combination of polynomial time transformations and queries is quite unique. Some of the queries can be answered directly using the switch-list input, others require a compilation of the input to OBDD representations which are then used to answer the queries.

This paper proposes a framework for analyzing algorithms for inductive processing of bi-connected graphs. The BIBOX algorithm for solving cooperative path-finding problems over bi-connected graphs is submitted for the suggested analysis. The algorithm proceeds according to a decomposition of a given bi-connected graph into handles. After finishing a handle, the handle is ruled out of consideration and the processing task is reduced to a task of the same type on a smaller graph. The handle decomposition for which the BIBOX algorithm performs best is theoretically identified. The conducted experimental evaluation confirms that the suggested theoretical analysis well corresponds to the real situation.