A note on the rainbow cycle cover problem

Networks ◽  
2018 ◽  
Vol 73 (1) ◽  
pp. 38-47 ◽  
Author(s):  
Jorge Moreno ◽  
Simone Martins ◽  
Yuri Frota
Keyword(s):  
Cycle Cover ◽  
Cover Problem

An Optimal Strategy for the Constrained Cycle Cover Problem

1999 ◽  
Vol 1 ◽  
pp. 48-60
Author(s):  
Gilles Pesant ◽  
Patrick Soriano
Keyword(s):  
Optimal Strategy ◽  
Cycle Cover ◽  
Cover Problem

New approximation algorithms for the minimum cycle cover problem

2019 ◽  
Vol 793 ◽  
pp. 44-58 ◽  
Author(s):  
Wei Yu ◽  
Zhaohui Liu ◽  
Xiaoguang Bao
Keyword(s):  
Approximation Algorithms ◽  
Cycle Cover ◽  
Cover Problem

Approximation Algorithms for the Min-Max Cycle Cover Problem With Neighborhoods

2020 ◽  
Vol 28 (4) ◽  
pp. 1845-1858 ◽  
Author(s):  
Lijia Deng ◽  
Wenzheng Xu ◽  
Weifa Liang ◽  
Jian Peng ◽  
Yingjie Zhou ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Cycle Cover ◽  
Cover Problem

scholarly journals Approximation of Euclidean k-size cycle cover problem

2014 ◽  
Vol 5 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Michael Khachay ◽  
Katherine Neznakhina
Keyword(s):  
Cycle Cover ◽  
Cover Problem

scholarly journals On the relationship between ATSP and the cycle cover problem

2007 ◽  
Vol 370 (1-3) ◽  
pp. 218-228 ◽  
Author(s):  
L. Sunil Chandran ◽  
L. Shankar Ram
Keyword(s):  
Cycle Cover ◽  
Cover Problem ◽  
The Relationship

The Bounded Cycle-Cover Problem

2001 ◽  
Vol 13 (2) ◽  
pp. 104-119 ◽  
Author(s):  
Dorit S. Hochbaum ◽  
Eli V. Olinick
Keyword(s):  
Cycle Cover ◽  
Cover Problem

scholarly journals SDP-Based Bounds for the Quadratic Cycle Cover Problem via Cutting-Plane Augmented Lagrangian Methods and Reinforcement Learning

2021 ◽  
Author(s):  
Frank de Meijer ◽  
Renata Sotirov
Keyword(s):  
Reinforcement Learning ◽  
Semidefinite Programming ◽  
Cutting Planes ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Cutting Plane ◽  
Projection Algorithm ◽  
Sdp Relaxation ◽  
Cycle Cover ◽  
Cover Problem

We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra’s projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra’s projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations.

The Rainbow Cycle Cover Problem

Networks ◽  
2016 ◽  
Vol 68 (4) ◽  
pp. 260-270 ◽  
Author(s):  
Selene Silvestri ◽  
Gilbert Laporte ◽  
Raffaele Cerulli
Keyword(s):  
Cycle Cover ◽  
Cover Problem
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