Clique-Based Deletion-Correcting Codes via Penalty-Guided Clique Search
Aniruddh Pandav, Rajshekhar V Bhat

TL;DR
This paper introduces a novel heuristic for constructing larger deletion-correcting codes by formulating the problem as a maximum clique search and applying a penalty-guided heuristic, outperforming existing methods and matching known optimal sizes.
Contribution
It proposes a penalty-guided clique search heuristic for constructing deletion-correcting codes, improving code sizes over existing graph-based heuristics and classical constructions.
Findings
PGCS yields larger codebooks than existing heuristics.
Codebooks match or exceed known optimal sizes for certain parameters.
Optimized LCS-based decoder reduces decoding complexity significantly.
Abstract
We study the construction of -deletion-correcting binary codes by formulating the problem as a Maximum Clique Problem (MCP). In this formulation, vertices represent candidate codewords and edges connect pairs whose longest common subsequence (LCS) distance guarantees correction of up to deletions. A valid codebook corresponds to a clique in the resulting graph, and finding the largest codebook is equivalent to identifying a maximum clique. While MCP-based formulations for deletion-correcting codes have previously been explored, we demonstrate that applying Penalty-Guided Clique Search (PGCS), a lightweight stochastic clique-search heuristic inspired by Dynamic Local Search (DLS), consistently yields larger codebooks than existing graph-based heuristics, including minimum-degree and coloring methods, for block lengths and deletion parameters . In…
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Taxonomy
TopicsDNA and Biological Computing · Advanced biosensing and bioanalysis techniques · Gene expression and cancer classification
