7 papers · 1 filter
Equivalent Dichotomies for Triangle Detection in Subgraph, Induced, and Colored H-Free Graphs
Amir Abboud, Ron Safier, Nathan Wallheimer
A recent paper by the authors (ITCS'26) initiates the study of the Triangle Detection problem in graphs avoiding a fixed pattern H as a subgraph and proposes a dichotomy hypothesis…
A Truly Subcubic Combinatorial Algorithm for Induced 4-Cycle Detection
Amir Abboud, Shyan Akmal, Nick Fischer
We present the first truly subcubic, combinatorial algorithm for detecting an induced -cycle in a graph. The running time is on -node graphs, thus separating th…
Triangle Detection in H-Free Graphs
Amir Abboud, Ron Safier, Nathan Wallheimer
We initiate the study of combinatorial algorithms for Triangle Detection in -free graphs. The goal is to decide if a graph that forbids a fixed pattern as a subgraph contain…
All-Pairs Shortest Paths with Few Weights per Node
Amir Abboud, Nick Fischer, Ce Jin +2
We study the central All-Pairs Shortest Paths (APSP) problem under the restriction that there are at most distinct weights on the outgoing edges from every node. For this…
Recognizing Sumsets is NP-Complete
Amir Abboud, Nick Fischer, Ron Safier +1
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set is a sumset, i.e. whether there is a s…
Worst-Case to Expander-Case Reductions: Derandomized and Generalized
Amir Abboud, Nathan Wallheimer
A recent paper by Abboud and Wallheimer [ITCS 2023] presents self-reductions for various fundamental graph problems, which transform worst-case instances to expanders, thus proving…