To formally define our problem, we are given a graph structure, G(V,E) of our cellular decomposition. V is the nodes set, which are the center points of each cell, and E is the edges set, which are the line segments connecting centers of adjacent cells. Each cell is decomposed to 4 sub-cells. We are also given initial locations of k robots on sub-cells of G’ cells. For every spanning tree of G, STG, moving along the path which circumnavigates STG orders the robots. Let Dij be the distance along the spanning tree path between two consecutive robots. Out problem is to find STG that minimizes max i∈kDijThe construction of an optimal spanning tree is believed to be N P-Hard [30]. However, an approximation algorithm (co-authored with Noa Agmon and Gal Kaminka) exists [2]. It is presented in Appendix A.
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