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We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…

Data Structures and Algorithms · Computer Science 2018-12-08 Christine Dahn , Nils M. Kriege , Petra Mutzel

We present SurfCut, an algorithm for extracting a smooth, simple surface with an unknown 3D curve boundary from a noisy 3D image and a seed point. Our method is built on the novel observation that certain ridge curves of a function defined…

Computer Vision and Pattern Recognition · Computer Science 2017-05-02 Marei Algarni , Ganesh Sundaramoorthi

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-12-10 Kevin Aydin , MohammadHossein Bateni , Vahab Mirrokni

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…

Data Analysis, Statistics and Probability · Physics 2009-09-29 Hristo Djidjev

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…

Data Structures and Algorithms · Computer Science 2017-04-04 Moses Charikar , Neha Gupta , Roy Schwartz

Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…

Data Structures and Algorithms · Computer Science 2020-12-18 Zhenyu Guo , Mingyu Xiao , Yi Zhou , Dongxiang Zhang , Kian-Lee Tan

We study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign…

Data Structures and Algorithms · Computer Science 2019-07-09 Stefan Kratsch , Shaohua Li , Dániel Marx , Marcin Pilipczuk , Magnus Wahlström

An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$…

Quantum Physics · Physics 2024-02-06 Simon Apers , Arinta Auza , Troy Lee

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

Computer Vision and Pattern Recognition · Computer Science 2012-03-14 Jan Egger , Tina Kapur , Thomas Dukatz , Malgorzata Kolodziej , Dzenan Zukic , Bernd Freisleben , Christopher Nimsky

We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…

Data Structures and Algorithms · Computer Science 2020-05-05 Julia Chuzhoy , Yu Gao , Jason Li , Danupon Nanongkai , Richard Peng , Thatchaphol Saranurak

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

Machine Learning · Statistics 2013-09-11 Jing Qian , Venkatesh Saligrama

The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…

Combinatorics · Mathematics 2023-08-15 Justo Puerto , José L. Sainz-Pardo

We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…

Data Structures and Algorithms · Computer Science 2020-01-01 Stephen Jue , Philip N. Klein

The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…

Data Structures and Algorithms · Computer Science 2022-03-01 Eiichiro Sato

The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…

Data Structures and Algorithms · Computer Science 2020-01-10 Nate Veldt , Austin R. Benson , Jon Kleinberg

There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal…

Other Computer Science · Computer Science 2018-07-26 Karlis Freivalds , Jans Glagolevs

MaxCut is a classical NP-complete problem and a crucial building block in many combinatorial algorithms. The famous Edwards-Erd\H{o}s bound states that any connected graph on n vertices with m edges contains a cut of size at least $m/2 +…

Data Structures and Algorithms · Computer Science 2024-07-02 Jonas Lill , Kalina Petrova , Simon Weber

The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…

Data Structures and Algorithms · Computer Science 2017-04-10 Augusto Bordini , Fábio Protti

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

Statistical Mechanics · Physics 2010-04-27 Allon G. Percus , Gabriel Istrate , Bruno Goncalves , Robert Z. Sumi , Stefan Boettcher

We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…

Data Structures and Algorithms · Computer Science 2018-02-21 Aditya Bhaskara , Samira Daruki , Suresh Venkatasubramanian