We obtain the first approximation algorithm for finding the k-simple shortest paths connecting a pair of vertices in a weighted directed graph. Our algorithm is deterministic and has a running time of O(k(m √ n + n log n)), where m is the number of edges in the graph and n is the number of vertices. Let s, t ∈ V ; the length of the i-th simple path from s to t computed by our algorithm is at mo...

Networks can be represented as evolutionary graphs in a variety of spatio-temporal applications. Changes in the nodes and edges over time may also result in corresponding changes in structural garph properties such as shortest path distances. In this paper, we study the problem of detecting the top-k most significant shortest-path distance changes between two snapshots of an evolving graph. Whi...

By repeatedly combining the source node's nearest neighbor, we propose a node combination (NC) method to implement the Dijkstra's algorithm. The NC algorithm finds the shortest paths with three simple iterative steps: find the nearest neighbor of the source node, combine that node with the source node, and modify the weights on edges that connect to the nearest neighbor. The NC algorithm is mor...

All Colors Shortest Path problem defined on an undirected graph aims at finding a shortest, possibly non-simple, path where every color occurs at least once, assuming that each vertex in the graph is associated with a color known in advance. To the best of our knowledge, this paper is the first to define and investigate this problem. Even though the problem is computationally similar to general...

We present eecient algorithms for shortest-path and minimum-link-path queries between two convex polygons inside a simple polygon P, which acts as an obstacle to be avoided. Let n be the number of vertices of P, and h the total number of vertices of the query polygons. We show that shortest-path queries can be performed optimally in time O(log h + logn) (plus O(k) time for reporting the k edges...

We present e cient algorithms for shortest path and minimum link path queries between two convex polygons inside a simple polygon P which acts as an obstacle to be avoided Let n be the number of vertices of P and h the total number of vertices of the query polygons We show that shortest path queries can be performed optimally in time O logh logn plus O k time for reporting the k edges of the pa...

The shortest path problem is solved and applied to the calculations of half lives with respect to spontaneous fission of heavy nuclei. The dynamical programming method of Bellman and Kalaba is used to find the fission path in the d-dimensional space of deformation parameters. Fission half lives of heavy isotopes (100<Z<110) are shown and compared to the experimental data. 1. Introductory remark...