English
Related papers

Related papers: Submodular Hypergraph Partitioning: Metric Relaxat…

200 papers

The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…

Numerical Analysis · Mathematics 2023-02-08 Lars Eldén

Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…

Data Structures and Algorithms · Computer Science 2023-09-28 Quanquan C. Liu , Jessica Shi , Shangdi Yu , Laxman Dhulipala , Julian Shun

In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…

Data Structures and Algorithms · Computer Science 2017-08-17 Ken-ichi Kawarabayashi , Anastasios Sidiropoulos

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…

Human-Computer Interaction · Computer Science 2024-10-28 Marina Evers , Lars Linsen

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…

Data Structures and Algorithms · Computer Science 2013-11-12 Samir Khuller , Manish Purohit , Kanthi Sarpatwar

Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…

Data Structures and Algorithms · Computer Science 2025-09-29 Slobodan Mitrović , Theodore Pan , Mahdi Qaempanah , Mohammad Amin Raeisi

Recent years have seen extensive research on directed graph sparsification. In this work, we initiate the study of fast fully dynamic spectral and cut sparsification algorithms for directed graphs. We introduce a new notion of spectral…

Data Structures and Algorithms · Computer Science 2025-07-29 Yibin Zhao

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Computational Complexity · Computer Science 2019-04-29 Andreas Emil Feldmann

Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where…

Machine Learning · Computer Science 2021-10-29 Nate Veldt , Austin R. Benson , Jon Kleinberg

We present the first work-optimal polylogarithmic-depth parallel algorithm for the minimum cut problem on non-sparse graphs. For $m\geq n^{1+\epsilon}$ for any constant $\epsilon>0$, our algorithm requires $O(m \log n)$ work and $O(\log^3…

Data Structures and Algorithms · Computer Science 2021-02-19 Andrés López-Martínez , Sagnik Mukhopadhyay , Danupon Nanongkai

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

Data Structures and Algorithms · Computer Science 2021-06-07 Nate Veldt , Austin R. Benson , Jon Kleinberg

The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an $O(\log…

Data Structures and Algorithms · Computer Science 2024-10-18 Laxman Dhulipala , Michael Dinitz , Jakub Łącki , Slobodan Mitrović

In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…

Computational Geometry · Computer Science 2021-10-11 Mariusz Wzorek , Cyrille Berger , Patrick Doherty

We give two new approximation algorithms to compute the fractional hypertree width of an input hypergraph. The first algorithm takes as input $n$-vertex $m$-edge hypergraph $H$ of fractional hypertree width at most $\omega$, runs in…

Data Structures and Algorithms · Computer Science 2024-10-01 Viktoriia Korchemna , Daniel Lokshtanov , Saket Saurabh , Vaishali Surianarayanan , Jie Xue

Distributed systems that manage and process graph-structured data internally solve a graph partitioning problem to minimize their communication overhead and query run-time. Besides computational complexity -- optimal graph partitioning is…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-03-24 Ruben Mayer , Hans-Arno Jacobsen

Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum…

Computer Vision and Pattern Recognition · Computer Science 2017-07-28 Margret Keuper

Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…

Optimization and Control · Mathematics 2023-11-17 Daniel Porumbel

Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…

Machine Learning · Computer Science 2019-05-15 Sejun Park , Eunho Yang , Se-Young Yun , Jinwoo Shin

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…

Computer Vision and Pattern Recognition · Computer Science 2018-02-07 Hanzi Wang , Guobao Xiao , Yan Yan , David Suter

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

Data Structures and Algorithms · Computer Science 2024-12-25 Marin Bougeret , Jérémy Omer , Michael Poss