LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Anytime algorithms for the longest common palindromic subsequence problem

The longest common palindromic subsequence (LCPS) problem aims at finding a longest string that appears as a subsequence in each of a set of input strings and is a palindrome at the same time. The problem is a special variant of the well known longest common subsequence problem and has applications in particular in genomics and biology, where strings correspond to DNA or protein sequences and similarities among them shall be detected or quantified. We first present a more traditional A* search that makes use of an advanced upper bound calculation for partial solutions. This exact approach works well for instances with two input strings and, as shown in experiments, outperforms several other exact methods from the literature. However, the A* search also has natural limitations when a larger number of strings shall be considered due to the problem's complexity. To effectively deal with this case in practice, anytime A* search variants are investigated, which are able to return a reasonable heuristic solution at almost any time and are expected to find better and better solutions until reaching a proven optimum when enough time given. In particular a novel approach is proposed in which Anytime Column Search (ACS) is interleaved with traditional A* node expansions. The ACS iterations are guided by a new heuristic function that approximates the expected length of an LCPS in subproblems usually much better than the available upper bound calculation. This A*+ACS hybrid is able to solve small to medium-sized LCPS instances to proven optimality while returning good heuristic solutions together with upper bounds for large instances. In rigorous experimental evaluations we compare A*+ACS to several other anytime A* search variants and observe its superiority.Doctoral Program “Vienna Graduate School on Computational Optimization” funded by the Austrian Science Foundation (FWF) under contract nr. W1260-N35

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Exact and Heuristic Approaches for Solving String Problems from Bioinformatics

Arbeit an der Bibliothek noch nicht eingelangt - Daten nicht geprüftAbweichender Titel nach Übersetzung der Verfasserin/des VerfassersThis thesis provides several new algorithms for solving prominent string problems from the literature, most of these being variants of the well-known longest common subsequence (LCS) problem. Given a set of input strings, a longest common subsequence is a string of maximum length that can be obtained from each input string by removing letters, i.e., which is a common subsequence of all input strings. The problem is known to be NP–hard and challenging to solve in practice for the general case of an arbitrary set of input strings. Besides the basic LCS problem variant, we consider here the following important variants: the longest common palindromic subsequence problem, the arc-preserving LCS problem, the longest common square subsequence problem, the repetition-free LCS problem, and the constrained LCS problem. These problems provide a range of important measures which serve for detecting similarities between molecules of various structures. Concerning heuristic approaches, we propose a general beam search framework in which many previously described methods from literature can be expressed. In particular, new state-of-the-art results were obtained on various benchmark sets utilizing a novel heuristic guidance that approximates the expected solution length of three different string problems. For solving the longest common square subsequence problem, a hybrid of a Reduced Variable Neighborhood Search method and a Beam search technique has been proposed. Concerning exact techniques, two kinds of methods are proposed: (i) pure exact methods based on A∗ search and (ii) anytime algorithms that build upon the A∗ search framework. Experimental results indicate that this A∗ search is also able to outperform all previously published more specific exact algorithms for the longest common palindromic subsequence and the constrained longest common subsequence problems with two input strings. Concerning anytime algorithms, we first make use of the derived A∗ search framework such that classical A∗ iterations are interleaved with beam search runs. Later, another anytime algorithm variant is proposed in which the beam search part is replaced by a major iteration of the Anytime Column Search. New state-of-the-art results are produced and better final optimality gaps were obtained by the latter hybrid, in comparison to a several state-of-the-art anytime algorithms from the literature. As an alternative exact approach, we further consider the transformation of LCS problem instances into Maximum Clique (MC) problem instance on the basis of so-called conflict graphs. In this way, state-of-the-art MC solvers can be utilized for solving the LCS problem instances. Further, an effective conflict graph reduction based on suboptimality checks is proposed. In conjunction with the general-purpose mixed integer linear programming solver Cplex, new state-of-the-art results are obtained on a wide range of benchmark instances.22

Exact and Heuristic Approaches for the Longest Common Palindromic Subsequence Problem

[EN]The longest common palindromic subsequence (LCPS) problem requires to find a longest palindromic string that appears as subsequence in each string from a given set of input strings. The algorithms that can be found in the related literature are specific for LCPS problems with only two input strings. In contrast, in this work we consider the general case with an arbitrary number of input strings, which is NP-hard. To solve this problem we propose a fast greedy heuristic, a beam search, and an exact A ∗ algorithm. Moreover, A ∗ is extended by a simple diving mechanism as well as a combination with beam search in order to find good quality solutions already early in the search process. The most important findings that result from the experimental evaluation include that (1) A ∗ is able to efficiently find proven optimal solutions for smaller problem instances, (2) the anytime behavior of A ∗ can be significantly improved by incorporating diving or beam search, and (3) beam search is best from a purely heuristic perspective.We gratefully acknowledge the financial support of this project by the Doctoral Program “Vienna Graduate School on Computational Optimization” funded by the Austrian Science Foundation (FWF) under contract no. W1260-N35.Peer reviewe