Let G=(V,E) be an undirected unweighted graph. A path between any two vertices u,v∈V is said to be t-approximate shortest path if its length is at most t times the length of the shortest path between u and v. We address the problem of building a compact data structure which can...
Starting from one point in the graph, we look at all the nodes one level away, then all the nodes two levels away, then all the nodes three levels away, and so on - until we’ve seen every node. Key Data Structure: The Queue ...
CISC 235: Topic 11 Shortest Paths Algorithms
Thorup and Zwick, in the seminal paper [Journal of ACM, 52(1), 2005, pp 1-24], showed that a weighted undirected graph on n vertices can be preprocessed in subcubic time to design a data structure which occupies only subquadratic space, and yet, for any pair of vertices, can answer ...
We study the {\\em min-cost chain-constrained spanning-tree} (abbreviated\\mcst) problem: find a min-cost spanning tree in a graph subject to degreeconstraints on a nested family of node sets. We devise the {\\em first} polytimealgorithm that finds a spanning tree that (i) violates ...