2026-08-17T05:00:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8144 2024-03-06T10:39:16Z ddc:004 open_access

Towards Hardness of Approximation for Polynomial Time Problems Abboud, Amir Backurs, Arturs LCS Edit Distance Hardness in P Proving hardness of approximation is a major challenge in the field of fine-grained complexity and conditional lower bounds in P. How well can the Longest Common Subsequence (LCS) or the Edit Distance be approximated by an algorithm that runs in near-linear time? In this paper, we make progress towards answering these questions. We introduce a framework that exhibits barriers for truly subquadratic and deterministic algorithms with good approximation guarantees. Our framework highlights a novel connection between deterministic approximation algorithms for natural problems in P and circuit lower bounds. In particular, we discover a curious connection of the following form: if there exists a \delta>0 such that for all \eps>0 there is a deterministic (1+\eps)-approximation algorithm for LCS on two sequences of length n over an alphabet of size n^{o(1)} that runs in O(n^{2-\delta}) time, then a certain plausible hypothesis is refuted, and the class E^NP does not have non-uniform linear size Valiant Series-Parallel circuits. Thus, designing a "truly subquadratic PTAS" for LCS is as hard as resolving an old open question in complexity theory. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Amir Abboud and Arturs Backurs 2017 Is Part Of LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2017.11 urn:nbn:de:0030-drops-81443 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.11 eng https://creativecommons.org/licenses/by/3.0/legalcode