Rebin Silva Valan Arasu

arXiv2026

A Configurable Heuristic for the MLCS Problem

Motivation: The Multiple Longest Common Subsequence (MLCS) problem for an arbitrary number of sequences is an NP-hard problem in sequence analysis. Existing exact algorithms based on dynamic programming or MLCS-DAG pruning rapidly exhaust memory as sequence lengths and set sizes grow, while heuristic and hyper-heuristic approaches compromise solution quality and require heavy parameter tuning, respectively. Results: This paper presents the ARP heuristic that, for a given primary sequence, performs three key actions: (i) Adding-$Δ$s, which incrementally builds a solution by adding subsequences, called $Δ$s, of the primary sequence to an initial solution; (ii) Replacing-Subsequences, which enhances the diversity of the solution set via targeted replacement of subsequences common to all solutions; and (iii) Prioritizing groups of characters from the primary sequence that are likely to appear together in longer common subsequences. ARP allows the user to configure the degree of Replacements and Prioritization actions for carrying out quality-runtime tradeoff. Empirical evaluations on both synthetic and biological sequence sets demonstrate that ARP's fastest configuration AOnly finds significantly longer common subsequences than the BNMAS classical heuristic and its aggressive configuration attains solution quality comparable to state-of-the-art hyper-heuristic (UB-HH) while running 1.1$\times$-1.7$\times$ faster.

cs.DC↗

arXiv2026

Solving Subgraph Extraction Problems Using $Δ$Search

Many NP-hard graph problems can be modeled as optimal subgraph extraction problems with feasibility constraints. From Network Design to Facility Location, from Robotics to Graph Drawing, the subgraph extraction pattern emerges across diverse domains. Despite this commonality, these problems are typically solved with domain-specific heuristics. Usually, these problems balance competing objectives such as maximizing coverage or minimizing cost while satisfying structural constraints such as connectivity, planarity and reachability. In this work, we introduce $Δ$Search, a general and fast heuristic framework that exploits the insight of Reward-Penalty optimization for solving a large class of subgraph extraction problems. The framework is easy to use as it only requires feasibility constraints and optimality criteria to be provided by the user to express the subgraph extraction problem. We also show how exact methods can be augmented with $Δ$Search to improve their performance by aggressive pruning of the search space. We evaluate our framework on monotone graph problems such as Maximum Planar Subgraph (MPS) and Minimum Connected Dominating Set, Weighted Monotone problems such as Maximum Weighted Independent Set and Minimum Weighted Steiner Tree, and non-monotone graph problems such as Prize Collecting Vertex Cover (PCVC) and Uncapacitated Facility Location Problem (UFLP). Our results show that $Δ$Search matches or surpasses state of the art heuristics for MPS, UFLP and PCVC problems with similar runtime. For the remaining problems, $Δ$Search achieves approximately 89% of the solution quality of the state-of-the-art algorithms without any problem-specific tuning

cs.PF↗