Abstract
It is known that many optimisation problems on networks are NP-hard. However, it seems that the real transport networks have some interesting properties which allow us to find a "good" solution in reasonable time. In this paper, we suggest and study some new parameters of the transportation networks which could be useful in optimisation problems. We define the evenness and the robustness of the solution. We also concern ourselves with the statistical distribution of distances and edge values in transportation networks.
Highlights
Introduction and preliminariesIt is well known fact that many optimisation algorithms work more successfully in real networks than in random graphs
We suggest and study some new parameters of the transportation networks which could be useful in optimisation problems
We concern ourselves with the statistical distribution of distances and edge values in transportation networks
Summary
It is well known fact that many optimisation algorithms work more successfully in real networks than in random graphs. Set D 1 V is the p-center of G, if D = p and ecG ^Dh # ecG ^Dlh for any p-element subset Dl 1 V. Set D 1 V is the weighted p-center of G, if D = p and eccG ^Dh # eccG ^Dlh for any p-element subset Dl 1 V. Set D 1 V is the anti-p-center of G, if D = p and ecG ^Dh # ecG ^Dlh or any p-element subset Dl 1 V. It is known that the mentioned problems are NP-hard (if p is a part of the input) [5 and 6] This is the reason why heuristic algorithms are usually used for finding a suboptimal solution [7, 8 and [9]. / The total weighted distance of vertices of G from D is f w G w^vh $ dG ^v, Dh
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