Abstract
The optimal link removal (OLR) problem aims at removing a given number of links of a network so that the spectral radius of the residue network obtained by removing the links from the network attains the minimum. Torus networks are a class of regular networks that have witnessed widespread applications. This paper addresses three subproblems of the OLR problem for torus networks, where two or three or four edges are removed. For either of the three subproblems, a link-removing scheme is described. Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem. Monte-Carlo simulations demonstrate that, for medium-sized tori, each of the three schemes produces a solution to the corresponding subproblem, which is optimal when compared to a large set of randomly produced link-removing schemes. Consequently, it is speculated that each of the three schemes produces an optimal solution to the corresponding subproblem for all torus networks. The set of links produced by each of our schemes is evenly distributed over a network, which may be a common feature of an optimal solution to the OLR problem for regular networks.
Highlights
The epidemic modeling is recognized as an effective approach to the understanding of propagation process of objects over a network [1, 2]
The optimal link removal (OLR) problem aims at removing a given number of links of a network so that the spectral radius of the residue network obtained by removing the links from the network attains the minimum
Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem
Summary
The epidemic modeling is recognized as an effective approach to the understanding of propagation process of objects over a network [1, 2]. There is no report in literature on the OLR problem for torus networks. Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem. Monte-Carlo simulations demonstates that, for medium-sized tori, each of the three schemes produces a solution to the corresponding subproblem, which is optimal when compared to 10,000 randomly produced sets of links. It is speculated that each of the three schemes produces an optimal solution to the corresponding subproblem for all torus networks. The set of links produced by each of our schemes is evenly distributed over a network, which may be a common feature of an optimal solution to the OLR problem for regular networks.
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