Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem

2021 ◽  
pp. 346-358
Author(s):  
Andrew Bloch-Hansen ◽  
Nasim Samei ◽  
Roberto Solis-Oba
Keyword(s):  
Approximation Algorithm ◽  
Local Search ◽  
Experimental Evaluation ◽  
Multiway Cut

A local search approximation algorithm for a squared metric k-facility location problem

2018 ◽  
Vol 35 (4) ◽  
pp. 1168-1184
Author(s):  
Dongmei Zhang ◽  
Dachuan Xu ◽  
Yishui Wang ◽  
Peng Zhang ◽  
Zhenning Zhang
Keyword(s):  
Approximation Algorithm ◽  
Local Search ◽  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem

scholarly journals A local search approximation algorithm for k-means clustering

2004 ◽  
Vol 28 (2-3) ◽  
pp. 89-112 ◽  
Author(s):  
Tapas Kanungo ◽  
David M. Mount ◽  
Nathan S. Netanyahu ◽  
Christine D. Piatko ◽  
Ruth Silverman ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Local Search

A 2-Approximation Algorithm for the Directed Multiway Cut Problem

2001 ◽  
Vol 31 (2) ◽  
pp. 477-482 ◽  
Author(s):  
Joseph (Seffi) Naor ◽  
Leonid Zosin
Keyword(s):  
Approximation Algorithm ◽  
Multiway Cut

scholarly journals A local search algorithm for the constrained max cut problem on hypergraphs.

2018 ◽  
Author(s):  
Nasim Samei ◽  
Roberto Solis-Oba
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Approximation Ratio ◽  
Local Search Algorithm ◽  
Multiway Cut ◽  
Max Cut Problem ◽  
Weighted Hypergraph

In the constrained max k-cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E), an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c. In this paper we present a local search algorithm for the constrained max k-cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c, such as for the constraints defining the max Steiner k-cut problem, the max multiway cut problem and the max k-cut problem. We also show that our local search algorithm can be used on the max k-cut problem with given sizes of parts and on the capacitated max k-cut problem, and has approximation ratio 1-|Vmax|/|V|, where |Vmax| is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k-cut problem that has approximation ratio (k-1)/(3k-2).

scholarly journals A local search algorithm for the constrained max cut problem on hypergraphs.

2018 ◽  
Author(s):  
Nasim Samei ◽  
Roberto Solis-Oba
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Approximation Ratio ◽  
Local Search Algorithm ◽  
Multiway Cut ◽  
Max Cut Problem ◽  
Weighted Hypergraph

In the constrained max k-cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E), an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c. In this paper we present a local search algorithm for the constrained max k-cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c, such as for the constraints defining the max Steiner k-cut problem, the max multiway cut problem and the max k-cut problem. We also show that our local search algorithm can be used on the max k-cut problem with given sizes of parts and on the capacitated max k-cut problem, and has approximation ratio 1-|Vmax|/|V|, where |Vmax| is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k-cut problem that has approximation ratio (k-1)/(3k-2).

A Local Search Approximation Algorithm for the k-means Problem with Penalties

2017 ◽  
pp. 568-574 ◽  
Author(s):  
Dongmei Zhang ◽  
Chunlin Hao ◽  
Chenchen Wu ◽  
Dachuan Xu ◽  
Zhenning Zhang
Keyword(s):  
Approximation Algorithm ◽  
Local Search
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