We study the min st-cut and max st-flow problems in planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph and two vertices s and… (More)

We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in O(log n/ log logn) amortized time and connectivity queries in… (More)

In a graph <i>G</i> with non-negative edge lengths, let <i>P</i> be a shortest path from a vertex <i>s</i> to a vertex <i>t</i>. We consider the problem of computing, for each edge <i>e</i> on… (More)

A spanner <i>H</i> of a weighted undirected graph <i>G</i> is a “sparse” subgraph that approximately preserves distances between every pair of vertices in <i>G</i>. We refer to <i>H</i> as a… (More)

We give an O(n logn) time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for… (More)

Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 2, we show that a (2k − 1)-approximate distance oracle for G of size O(kn) and with O(log… (More)

Given an n-vertex planar directed graph with real edge lengths and with no negative cycles, we show how to compute single-source shortest path distances in the graph in O(n log n/ log log n) time… (More)

2012 IEEE 53rd Annual Symposium on Foundations of…

2012

Let G = (V, E) be a planar n-vertex digraph. Consider the problem of computing max st-flow values in G from a fixed source s to all sinks t ϵ V \ {s}. We show how to solve this problem in near-linear… (More)