A tight bound for shortest augmenting paths on trees

A Tight Bound for Shortest Augmenting Paths on Trees

This paper is devoted to understanding the shortest augmenting path approach for computing a maximum matching. Despite its apparent potential for designing efficient matching and flow algorithms, it has been poorly understood. Chaudhuri et. al. [CDKL09] study this classical approach in the following model. A bipartite graph G = W ] B is revealed online and in each round a vertex of b is present...

Shortest - Paths Trees ∗

Tight Hardness for Shortest Cycles and Paths in Sparse Graphs

Fine-grained reductions have established equivalences between many core problems with Õ(n3)-time algorithms on n-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second Shortest Paths, and so on. These problems also have Õ(mn)-time algorithms on m-edge n-node weighted graphs, and such algorithms have wider applicability. Are these mn boun...

Tight bound on the maximum number of shortest unique substrings

A substring Q of a string S is called a shortest unique substring (SUS) for position p in S, if Q occurs exactly once in S, this occurrence of Q contains position p, and every substring of S which contains position p and is shorter than Q occurs at least twice in S. The SUS problem is, given a string S, to preprocess S so that for any subsequent query position p all the SUSs for position p can ...

Shortest paths on a polyhedron, Part I: Computing shortest paths

We present an algorithm for determining the shortest path between any two points along the surface of a polyhedron which need not be convex. This algorithm also computes for any source point on the surface of a polyhedron the inward layout and the subdivision of the polyhedron which can be used for processing queries of shortest paths between the source point and any destination point. Our algo...