Faster Combinatorial k-Clique Algorithms
Detecting if a graph contains ak-Clique is one of the most fundamental problems in
computer science. The asymptotically fastest algorithm runs in time O (n ω k/3), where ω is …
computer science. The asymptotically fastest algorithm runs in time O (n ω k/3), where ω is …
A Refutation of the Pach-Tardos Conjecture for 0-1 Matrices
S Pettie, G Tardos - arXiv preprint arXiv:2407.02638, 2024 - arxiv.org
The theory of forbidden 0-1 matrices generalizes Turan-style (bipartite) subgraph avoidance,
Davenport-Schinzel theory, and Zarankiewicz-type problems, and has been influential in …
Davenport-Schinzel theory, and Zarankiewicz-type problems, and has been influential in …
A Strongly Subcubic Combinatorial Algorithm for Triangle Detection with Applications
A Dumitrescu - arXiv preprint arXiv:2403.01085, 2024 - arxiv.org
We revisit the algorithmic problem of finding a triangle in a graph: We give a randomized
combinatorial algorithm for triangle detection in a given $ n $-vertex graph with $ m $ edges …
combinatorial algorithm for triangle detection in a given $ n $-vertex graph with $ m $ edges …
Range Longest Increasing Subsequence and its Relatives: Beating Quadratic Barrier and Approaching Optimality
S Rahul - arXiv preprint arXiv:2404.04795, 2024 - arxiv.org
In this work, we present a plethora of results for the range longest increasing subsequence
problem (Range-LIS) and its variants. The input to Range-LIS is a sequence $\mathcal {S} …
problem (Range-LIS) and its variants. The input to Range-LIS is a sequence $\mathcal {S} …
Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems
B Hu, A Polak - arXiv preprint arXiv:2409.15970, 2024 - arxiv.org
Most of the known tight lower bounds for dynamic problems are based on the Online
Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and …
Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and …
From Donkeys to Kings in Tournaments
A tournament is an orientation of a complete graph. A vertex that can reach every other
vertex within two steps is called a\emph {king}. We study the complexity of finding $ k $ kings …
vertex within two steps is called a\emph {king}. We study the complexity of finding $ k $ kings …
Robust Algorithms for Finding Triangles and Computing the Girth in Unit Disk and Transmission Graphs
K Klost, W Mulzer - arXiv preprint arXiv:2405.01180, 2024 - arxiv.org
We describe optimal robust algorithms for finding a triangle and the unweighted girth in a
unit disk graph, as well as finding a triangle in a transmission graph. In the robust setting, the …
unit disk graph, as well as finding a triangle in a transmission graph. In the robust setting, the …
Matchings, Maxflows, Matroids: The Power of Augmenting Paths and Computational Models
J Blikstad - 2024 - diva-portal.org
Abstract Matchings, Maximum Flow, and Matroid Intersections are fundamental
combinatorial optimization problems that have been studied extensively since the inception …
combinatorial optimization problems that have been studied extensively since the inception …