scholarly journals Hardness of covering all the triangles

2018 ◽  
Author(s):  
Thinh D. Nguyen
Keyword(s):  
Combinatorial Optimization ◽  
Polynomial Time ◽  
Optimization Problem ◽  
Vertex Cover ◽  
Research Area ◽  
Combinatorial Optimization Problem ◽  
Edge Cover ◽  
Hard Edge ◽  
Problem Solvability

Vertex Cover and Edge Cover are two classical examples that are often used to show the contrast of problem solvability. While Vertex Cover is hard, Edge Cover can be solved in polynomial time. We claim that the former remains intractable even if the objects to be covered are triangles instead of edges. Therefore, one more combinatorial optimization problem, namely Covering Triangles, is added to the decades-old list of the problems in this research area.

Inverse version of the kth maximization combinatorial optimization problem

2018 ◽  
Vol 54(5) ◽  
pp. 72
Author(s):  
Quoc, H.D. ◽  
Kien, N.T. ◽  
Thuy, T.T.C. ◽  
Hai, L.H. ◽  
Thanh, V.N.
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem

scholarly journals ANALYSIS AND SYNTHESIS OF ENHANCED ANT COLONY OPTIMIZATION WITH THE TRADITIONAL ANT COLONY OPTIMIZATION TO SOLVE TRAVELLING SALES PERSON PROBLEM

2011 ◽  
Vol 1 (1) ◽  
pp. 88-92
Author(s):  
Pallavi Arora ◽  
Harjeet Kaur ◽  
Prateek Agrawal
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Optimization Problem ◽  
Traditional Approach ◽  
Combinatorial Optimization Problem ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Analysis And Synthesis ◽  
Heuristic Technique ◽  
Travelling Salesperson Problem

Ant Colony optimization is a heuristic technique which has been applied to a number of combinatorial optimization problem and is based on the foraging behavior of the ants. Travelling Salesperson problem is a combinatorial optimization problem which requires that each city should be visited once. In this research paper we use the K means clustering technique and Enhanced Ant Colony Optimization algorithm to solve the TSP problem. We show a comparison of the traditional approach with the proposed approach. The simulated results show that the proposed algorithm is better compared to the traditional approach.

Ant Colony Optimization and Multiple Knapsack Problem

2007 ◽  
pp. 498-509 ◽  
Author(s):  
S. Fidanova
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Knapsack Problem ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Ant Colony ◽  
Multiple Knapsack Problem ◽  
Constraint Problem ◽  
Multiple Knapsack ◽  
Ant Colony Optimization Algorithms

The ant colony optimization algorithms and their applications on the multiple knapsack problem (MKP) are introduced. The MKP is a hard combinatorial optimization problem with wide application. Problems from different industrial fields can be interpreted as a knapsack problem including financial and other management. The MKP is represented by a graph, and solutions are represented by paths through the graph. Two pheromone models are compared: pheromone on nodes and pheromone on arcs of the graph. The MKP is a constraint problem which provides possibilities to use varied heuristic information. The purpose of the chapter is to compare a variety of heuristic and pheromone models and different variants of ACO algorithms on MKP.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

2006 ◽  
Vol 129 (2) ◽  
pp. 252-255
Author(s):  
Atanu K. Mohanty ◽  
Kanad Chakraborty ◽  
Anindya Chatterjee
Keyword(s):  
Combinatorial Optimization ◽  
Dynamic Systems ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
High Dimensional ◽  
Experimental Characterization ◽  
State Behavior ◽  
Simultaneous Measurements ◽  
Proper Orthogonal

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

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