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In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS…

Data Structures and Algorithms · Computer Science 2021-06-04 Jason Li , Thatchaphol Saranurak

We obtain faster expander decomposition algorithms for directed graphs, matching the guarantees of Saranurak and Wang (SODA 2019) for expander decomposition on undirected graphs. Our algorithms are faster than prior work and also generalize…

Data Structures and Algorithms · Computer Science 2025-11-11 Henry Fleischmann , George Z. Li , Jason Li

Despite that going deep has proven successful in many neural architectures, the existing graph transformers are relatively shallow. In this work, we explore whether more layers are beneficial to graph transformers, and find that current…

Machine Learning · Computer Science 2023-03-02 Haiteng Zhao , Shuming Ma , Dongdong Zhang , Zhi-Hong Deng , Furu Wei

We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between. These decompositions form critical subroutines in a number of graph algorithms.…

Data Structures and Algorithms · Computer Science 2013-07-16 Gary L. Miller , Richard Peng , Shen Chen Xu

In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle.…

Computational Complexity · Computer Science 2025-04-29 Cheng-Hao Fu , Andrea Lincoln , Rene Reyes

We construct worst-case examples for the standard reduction algorithm for computing persistent homology. Our constructions are similar to the worst-case examples introduced by Morozov, but we replace the single-triangle arrangement with a…

Algebraic Topology · Mathematics 2026-03-18 Uzay Çetin , Ergun Yalcin

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Machine Learning · Computer Science 2024-06-05 Hongkang Li , Meng Wang , Tengfei Ma , Sijia Liu , Zaixi Zhang , Pin-Yu Chen

We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…

Data Structures and Algorithms · Computer Science 2010-11-09 Aleksander Madry

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…

Data Structures and Algorithms · Computer Science 2016-05-04 Søren Dahlgaard

Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…

Computational Complexity · Computer Science 2012-02-20 Arnaud Casteigts , Bernard Mans , Luke Mathieson

Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…

Discrete Mathematics · Computer Science 2017-04-04 Zdeněk Dvořák

Whether a graph $G=(V,E)$ is connected is arguably its most fundamental property. Naturally, connectivity was the first characteristic studied for dynamic graphs, i.e. graphs that undergo edge insertions and deletions. While connectivity…

Data Structures and Algorithms · Computer Science 2025-10-10 Simon Meierhans , Maximilian Probst Gutenberg

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…

Data Structures and Algorithms · Computer Science 2018-10-26 Sebastian Lamm , Christian Schulz , Darren Strash , Robert Williger , Huashuo Zhang

Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…

Optimization and Control · Mathematics 2025-08-05 Parth Brahmbhatt , David L. Cole , Victor M. Zavala , Styliani Avraamidou

Expander decompositions form the basis of one of the most flexible paradigms for close-to-linear-time graph algorithms. Length-constrained expander decompositions generalize this paradigm to better work for problems with lengths, distances…

Data Structures and Algorithms · Computer Science 2024-05-16 Bernhard Haeupler , D Ellis Hershkowitz , Zihan Tan

The gap between the known randomized and deterministic local distributed algorithms underlies arguably the most fundamental and central open question in distributed graph algorithms. In this paper, we develop a generic and clean recipe for…

Data Structures and Algorithms · Computer Science 2019-09-19 Mohsen Ghaffari , David G. Harris , Fabian Kuhn

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…

Machine Learning · Computer Science 2022-03-17 Ismail R. Alkhouri , George K. Atia , Alvaro Velasquez

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Image and Video Processing · Electrical Eng. & Systems 2023-07-19 Diego Valsesia , Giulia Fracastoro , Enrico Magli

There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…

Computational Geometry · Computer Science 2016-10-28 Franz J. Brandenburg