A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Agrawal, Anadi; Gawrychowski, Paweł

doi:10.4230/lipics.isaac.2020.4

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analogously to Longest Common Subsequence, we derive similar hardness results for the related problems Longest Common Weakly Increasing Subsequence and Longest Common Increasing Subsequence. Both problems can be solved in slightly subquadratic time [7,23]. For Longest Common Increasing Subsequence, our lower bound was already shown by Duraj et al [24].…”

Section: Proof Let (I Ovsupporting

confidence: 62%

Parameterized Lower Bounds for Problems in P via Fine-Grained Cross-Compositions

Heeger¹,

Nichterlein²,

Niedermeier³

2023

Preprint

View full text Add to dashboard Cite

We provide a general framework to exclude parameterized running times of the form O( β + n γ ) for problems that have polynomial running time lower bounds under hypotheses from fine-grained complexity. Our framework is based on cross-compositions from parameterized complexity. We (conditionally) exclude running times of the form O( γ/(γ−1)−ε + n γ ) for any 1 < γ < 2 and ε > 0 for the following problems:Longest Common (Increasing) Subsequence: Given two length-n strings over an alphabet Σ (over N) and ∈ N, is there a common (increasing) subsequence of length in both strings? Discrete Fréchet Distance: Given two lists of n points each and k ∈ N , is the Fréchet distance of the lists at most k? Here is the maximum number of points which one list is ahead of the other list in an optimum traversal. Planar Motion Planning: Given a set of n non-intersecting axis-parallel line segment obstacles in the plane and a line segment robot (called rod), can the rod be moved to a specified target without touching any obstacles? Here is the maximum number of segments any segment has in its vicinity. Moreover, we exclude running times O( 2γ/(γ−1)−ε + n γ ) for any 1 < γ < 3 and ε > 0 for: Negative Triangle: Given an edge-weighted graph with n vertices, is there a triangle whose sum of edge-weights is negative? Here is the order of a maximum connected component. Triangle Collection: Given a vertex-colored graph with n vertices, is there for each triple of colors a triangle whose vertices have these three colors? Here is the order of a maximum connected component. 2nd Shortest Path: Given an n-vertex edge-weighted directed graph, two vertices s and t, and k ∈ N, has the second longest s-t-path length at most k? Here is the directed feedback vertex set number.Except for 2nd Shortest Path all these running time bounds are tight, that is, algorithms with running time O( γ/(γ−1) + n γ ) for any 1 < γ < 2 and O( 2γ/(γ−1) + n γ ) for any 1 < γ < 3, respectively, are known. Our running time lower bounds also imply lower bounds on kernelization algorithms for these problems.

show abstract

Section: Proof Let (I Ovsupporting

confidence: 62%