Escaping a grid by edge-disjoint paths

Abstract

We study the edge-disjoint escape problem in grids. Given a set of n sources in a two-dimensional grid, the problem is to connect all sources to the grid boundary using a set of n edge-disjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we solve the problem by first ensuring that no rectangle in the grid contain more sources than outlets, a necessary and sufficient condition for the existence of a solution. Based on this condition, we give a greedy algorithm that finds the paths in O(n 2) time, which is faster than all previous approaches. This problem finds applications in point-to-point delivery, VLSI reconfiguration, and package routing.