scholarly journals A Heuristic Algorithm for Optimal Hamiltonian Cycles in Weighted Graphs

2015 ◽  
Vol 11 (6) ◽  
pp. 5300-5305
Author(s):  
Tadeusz Ostrowski ◽  
Petroula Mavrikiou
Keyword(s):  
Heuristic Algorithm ◽  
Weighted Graph ◽  
Payoff Matrix ◽  
Difficulty Level ◽  
Hamiltonian Cycles ◽  
Weight Losses ◽  
Time Distance ◽  
Np Complete ◽  
The Traveling Salesman Problem ◽  
General Graphs

Abstract. The paper focuses on finding of the optimal Hamiltonian cycle, when it is regarded with respect to cost, time, distance or difficulty level of the route. The problem is strictly related to the traveling salesman problem proved to be NP-complete for general graphs. The paper gives a heuristic algorithm for finding the optimal spanning cycle in a weighted graph. Its idea is based on optimization of weight losses and reduction the complexity of a problem by reduction the dimension of the graph payoff matrix. 

A Two Stage Method for the Multiple Traveling Salesman Problem

2020 ◽  
Vol 11 (3) ◽  
pp. 79-91
Author(s):  
Azcarie Manuel Cabrera Cuevas ◽  
Jania Astrid Saucedo Martínez ◽  
José Antonio Marmolejo Saucedo
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Difficulty Level ◽  
Median Problem ◽  
Two Stage ◽  
Multiple Traveling Salesman Problem ◽  
Solution Methods ◽  
The Many ◽  
The Traveling Salesman Problem

The variation of the traveling salesman problem (TSP) with multiple salesmen (m-TSP) has been studied for many years resulting in diverse solution methods, both exact and heuristic. However, the high difficulty level on finding optimal (or acceptable) solutions has opposed the many efforts of doing so. The proposed method regards a two stage procedure which implies a modified version of the p-Median Problem (PMP) alongside the TSP, making a partition of the nodes into subsets that will be assigned to each salesman, solving it with Branch & Cut (B&C), in the first stage. This is followed by the routing, applying an Ant Colony Optimization (ACO) metaheuristic algorithm to solve a TSP for each subset of nodes. A case study was reviewed, detailing the positioning of five vehicles in strategic places in the Mexican Republic.

A O(m) Self-Stabilizing Algorithm for Maximal Triangle Partition of General Graphs

2017 ◽  
Vol 27 (02) ◽  
pp. 1750004
Author(s):  
Brahim Neggazi ◽  
Volker Turau ◽  
Mohammed Haddad ◽  
Hamamache Kheddouci
Keyword(s):  
Graph Matching ◽  
Partition Problem ◽  
Matching Problem ◽  
Np Complete ◽  
General Graphs

The triangle partition problem is a generalization of the well-known graph matching problem consisting of finding the maximum number of independent edges in a given graph, i.e., edges with no common node. Triangle partition instead aims to find the maximum number of disjoint triangles. The triangle partition problem is known to be NP-complete. Thus, in this paper, the focus is on the local maximization variant, called maximal triangle partition (MTP). Thus, paper presents a new self-stabilizing algorithm for MTP that converges in O(m) moves under the unfair distributed daemon.

CONNECTED LIAR'S DOMINATION IN GRAPHS: COMPLEXITY AND ALGORITHMS

2013 ◽  
Vol 05 (04) ◽  
pp. 1350024 ◽  
Author(s):  
B. S. PANDA ◽  
S. PAUL
Keyword(s):  
Dominating Set ◽  
Chordal Graphs ◽  
Hardness Of Approximation ◽  
Induced Subgraph ◽  
Path Graph ◽  
Block Graphs ◽  
Domination Problem ◽  
Np Complete ◽  
Domination In Graphs ◽  
General Graphs

A subset L ⊆ V of a graph G = (V, E) is called a connected liar's dominating set of G if (i) for all v ∈ V, |NG[v] ∩ L| ≥ 2, (ii) for every pair u, v ∈ V of distinct vertices, |(NG[u]∪NG[v])∩L| ≥ 3, and (iii) the induced subgraph of G on L is connected. In this paper, we initiate the algorithmic study of minimum connected liar's domination problem by showing that the corresponding decision version of the problem is NP-complete for general graph. Next we study this problem in subclasses of chordal graphs where we strengthen the NP-completeness of this problem for undirected path graph and prove that this problem is linearly solvable for block graphs. Finally, we propose an approximation algorithm for minimum connected liar's domination problem and investigate its hardness of approximation in general graphs.

scholarly journals K-Core Maximization: An Edge Addition Approach

2019 ◽  
Author(s):  
Zhongxin Zhou ◽  
Fan Zhang ◽  
Xuemin Lin ◽  
Wenjie Zhang ◽  
Chen Chen
Keyword(s):  
Heuristic Algorithm ◽  
Real Life ◽  
Optimization Techniques ◽  
Adjacent Vertex ◽  
Np Hard ◽  
Induced Subgraph ◽  
The Stability ◽  
General Graphs ◽  
Core Problem ◽  
Edge Addition

A popular model to measure the stability of a network is k-core - the maximal induced subgraph in which every vertex has at least k neighbors. Many studies maximize the number of vertices in k-core to improve the stability of a network. In this paper, we study the edge k-core problem: Given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A heuristic algorithm is proposed on general graphs with effective optimization techniques. Comprehensive experiments on 9 real-life datasets demonstrate the effectiveness and the efficiency of our proposed methods.

scholarly journals Complexity results on graphs with few cliques

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Bill Rosgen ◽  
Lorna Stewart
Keyword(s):  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Polynomial Time Algorithms ◽  
Helly Property ◽  
Graph Class ◽  
International Audience ◽  
Edge Clique Cover ◽  
Np Complete ◽  
General Graphs ◽  
Clique Problem

Graphs and Algorithms International audience A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection representation that satisfies the Helly property. On any such class of graphs, some problems that are NP-complete on general graphs, such as the maximum clique problem and the maximum weighted clique problem, admit polynomial time algorithms. Other problems, such as the vertex clique cover and edge clique cover problems remain NP-complete on these classes. Several classes of graphs which have few cliques are discussed, and the complexity of some partitioning and covering problems are determined for the class of all graphs which have fewer cliques than a given polynomial bound.

scholarly journals A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1300
Author(s):  
Uroš Čibej ◽  
Luka Fürst ◽  
Jurij Mihelič
Keyword(s):  
Symmetry Breaking ◽  
Optimization Problem ◽  
Heuristic Method ◽  
Search Space ◽  
Search Tree ◽  
Backtracking Search ◽  
Complete Problems ◽  
Np Complete ◽  
Complexity Hierarchy ◽  
General Graphs

We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential. We also position the optimization problem into the computational-complexity hierarchy. In particular, we show that the verifier lies between P and NP -complete problems. Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles.

scholarly journals Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

Global distribution center number of some graphs and an algorithm

2019 ◽  
Vol 53 (4) ◽  
pp. 1217-1227
Author(s):  
Rafet Durgut ◽  
Hakan Kutucu ◽  
Tufan Turaci
Keyword(s):  
Polynomial Time ◽  
Heuristic Algorithm ◽  
Distribution Center ◽  
Global Distribution ◽  
Minimum Cardinality ◽  
Global Center ◽  
General Graphs

The global center is a newly proposed graph concept. For a graph G = (V(G), E(G)), a set S ⊆ V(G) is a global distribution center if every vertex v ∈ V(G)\S is adjacent to a vertex u ∈ S with |N[u] ∩ S| ≥ |N[v] ∩ (V(G)\S)|, where N(v) = {u ∈ V(G)|uv ∈ E(G)} and N[v] = N(v) ∪ {v}. The global distribution center number of a graph G is the minimum cardinality of a global distribution center of G. In this paper, we investigate the global distribution center number for special families of graphs. Furthermore, we develop a polynomial time heuristic algorithm to find the set of the global distribution center for general graphs.

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