Convex geometries over induced paths with bounded length

Length-bounded disjoint paths in planar graphs

Efficiently Listing Bounded Length st-Paths

The problem of listing the K shortest simple (loopless) stpaths in a graph has been studied since the early 1960s. For a nonnegatively weighted graph with n vertices and m edges, the most efficient solution is an O(K(mn+n log n)) algorithm for directed graphs by Yen and Lawler [Management Science, 1971 and 1972], and an O(K(m+ n log n)) algorithm for the undirected version by Katoh et al. [Netw...

Reachability by paths of bounded curvature in a convex polygon

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P , we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n) time algorithm to co...

An Approximation Algorithm for General Minimum-length Bounded-curvature Paths

Prior approximation algorithms find an approximation to the shortest robust bounded-curvature path. We eliminate the condition that the approximated path is robust. Introduction. A differentiable path has curvature at most c if two circles of radius c can be placed tangent to any given point on the path (see Figure 1(a)), which restricts how quickly the path turns left or right. Such paths mode...

Disjoint paths of bounded length in large generalized cycles

A generalized p-cycle is a digraph whose set of vertices is partitioned in p parts that can bc ordered in such a way that a vertex is adjacent only to vertices in the next part. The families of B G C ( p , d , d ' ) and KGC(p ,d ,d "~ + d ' ) are the largest known p-cycles for their degree and diameter. [n this paper we present a lower bound for the fault-diameter of a generalized cycle. Then w...