In this study we consider the shortest path problem, where arc costs are subject to distributional uncertainty. Basically, decision-maker attempts minimize her worst-case expected loss over an ambiguity set (or a family) of candidate distributions that consistent with decision-maker’s initial information. The is formed by all satisfy prescribed linear first-order moment constraints respect subs...

In real-world optimization problems, effective path planning is important. The Shortest Path Problem (SPP) model a classical operations research that can be applied to determine an efficient from the starting point end in plan. However, real world, uncertainty often encountered and must faced. Significant factors problem of determining shortest are problems difficult predict, therefore new crit...

The shortest path tour problem (SPTP) consists of finding a shortest path from a given origin node s to a given destination node d in a directed graph with nonnegative arc lengths with the constraint that the optimal path P should successively pass through at least one node from given node subsets T1, T2, . . . , TN , where ⋂N k=1 Tk = ∅. In this paper, it will proved that the SPTP belongs to t...

It has been shown by Alon et al. that the so-called ‘all-pairs shortest-path’ problem can be solved in O((MV ) log(V )) for graphs with V vertices, with integer distances bounded by M . We solve the more general problem for graphs in R (assuming no negative cycles), with expected-case running time O(V 2.5 log(V )). While our result appears to violate the Ω(V ) requirement of “Funny Matrix Multi...

Social networking is gaining enormous popularity in the past few years. However, the popularity may also bring unexpected consequences for users regarding safety and privacy concerns. To prevent privacy being breached and modeling a social network as a weighted graph, many effective anonymization techniques have been proposed. In this work, we consider the edge weight anonymity problem. In part...

We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees can be compactly represented by a partially ordered set. We calculate the shortest distance along each candidate path by converting the problem into one of ...