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Related papers: Approximation Algorithms for Norm Multiway Cut

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We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

Data Structures and Algorithms · Computer Science 2025-12-17 Ron Mosenzon

The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three…

Data Structures and Algorithms · Computer Science 2024-03-22 Amit Chakrabarti , Andrew McGregor , Anthony Wirth

Whether or not the Sparsest Cut problem admits an efficient $O(1)$-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut,…

Data Structures and Algorithms · Computer Science 2025-10-01 Tommaso d'Orsi , Chris Jones , Jake Ruotolo , Salil Vadhan , Jiyu Zhang

Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…

Data Structures and Algorithms · Computer Science 2021-05-06 Lars Gottesbüren , Tobias Heuer , Peter Sanders , Christian Schulz , Daniel Seemaier

The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an…

Data Structures and Algorithms · Computer Science 2019-05-27 Yasuaki Kobayashi , Yusuke Kobayashi , Shuichi Miyazaki , Suguru Tamaki

We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…

Machine Learning · Computer Science 2018-02-21 Vishesh Jain , Frederic Koehler , Elchanan Mossel

We study the \emph{multiterminal cut} problem, which, given an $n$-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total…

Data Structures and Algorithms · Computer Science 2017-11-20 Yixin Cao , Jianer Chen , Jia-Hao Fan

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

Quantum Physics · Physics 2014-11-17 Edward Farhi , Jeffrey Goldstone , Sam Gutmann

We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…

Data Structures and Algorithms · Computer Science 2018-04-09 Karthekeyan Chandrasekaran , Matthias Mnich , Sahand Mozaffari

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…

Data Structures and Algorithms · Computer Science 2014-05-23 Danupon Nanongkai

We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each…

Numerical Analysis · Mathematics 2026-03-31 Lei Li , Yunxiao Liu , Chenchen Wan

We propose a preprocessing algorithm for the multiway cut problem that establishes its polynomial kernelizability when the difference between the parameter $k$ and the size of the smallest isolating cut is at most $log(k)$. To the best of…

Discrete Mathematics · Computer Science 2011-05-03 Igor Razgon

We discuss a new algorithmic type of problem in random graphs studying the minimum number of queries one has to ask about adjacency between pairs of vertices of a random graph $G\sim {\mathcal G}(n,p)$ in order to find a subgraph which…

Combinatorics · Mathematics 2016-08-05 Asaf Ferber , Michael Krivelevich , Benny Sudakov , Pedro Vieira

We study the classical NP-hard problems of finding maximum-size subsets from given sets of $k$ terminal pairs that can be routed via edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in a given graph. The approximability of…

Data Structures and Algorithms · Computer Science 2016-05-23 Krzysztof Fleszar , Matthias Mnich , Joachim Spoerhase

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

Data Structures and Algorithms · Computer Science 2025-09-10 Shangqi Lu , Yufei Tao

We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs. Our oracle model is inspired by the submodular function minimization problem: on query $S \subset V$, the oracle returns the…

Data Structures and Algorithms · Computer Science 2019-08-07 Aviad Rubinstein , Tselil Schramm , S. Matthew Weinberg

We consider the maximum matching problem in the semi-streaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a two-pass $(1/2 + 1/16)$-approximation…

Data Structures and Algorithms · Computer Science 2017-04-24 Sagar Kale , Sumedh Tirodkar

Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…

Data Structures and Algorithms · Computer Science 2018-03-09 Yinhui Cai , Guangting Chen , Yong Chen , Randy Goebel , Guohui Lin , Longcheng Liu , An Zhang

With the rapid growth of data in modern applications, parallel algorithms for maximizing non-monotone submodular functions have gained significant attention. In the parallel computation setting, the state-of-the-art approximation ratio of…

Data Structures and Algorithms · Computer Science 2025-10-07 Yixin Chen , Wenjing Chen , Alan Kuhnle

We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…

Data Structures and Algorithms · Computer Science 2020-04-27 Monika Henzinger , Alexander Noe , Christian Schulz