Connecting Obstacles in Vertex-Disjoint Paths
نویسندگان
چکیده
Given a set of k disjoint convex polygonal obstacles inside a triangular container, we add straight-line noncrossing edges such that each obstacle has three vertex-disjoint paths to the container. We prove combinatorial bounds on the minimum number of edges that are always sufficient and sometimes necessary. Figure 1: A triangular container with disjoint convex obstacles.
منابع مشابه
Analysis of an ( )-Approximation Algorithm for the Maximum Edge-Disjoint Paths Problem with Congestion Two
The edge-disjoint paths problem (EDPP) has been studied for a long time by graph theorists and algorithm developers for combinatorial optimization. In its most basic form, the EDPP is as follows: given a graph and a set of pairs of vertices/terminals for in decide whether or not has edge-disjoint paths connecting the given pairs of terminals. This problem is equivalent to finding vertex-disjoin...
متن کاملFinding Common Ancestors and Disjoint Paths in DAGs
We consider the problem of finding pairs of vertex-disjoint paths in a DAG, either connecting two given nodes to a common ancestor, or connecting two given pairs of terminals. It was known how to find a single pair of paths, for either type of input, in polynomial time. We show how to find the k pairs with shortest combined length, in time O(mn + k). We also show how to count all such pairs of ...
متن کاملApplications of a Numbering Scheme for Polygonal Obstacles in the Plane
Danny Z. Chen! We present efficient algorithms for the problems of matching red and blue disjoint geometric obstacles in the plane and connecting the matched obstacle pairs with mutually noninlersecl.ing paths that have useful geometric properties. We first consider matching n red and n blue disjoint isothctic rectangles and connecting tile n matched rectangle pairs with noninlersecting monoton...
متن کاملMany-to-Many Disjoint Path Covers in Two-Dimensional Bipartite Tori with a Single Vertex Fault
A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faul...
متن کاملAlgorithms for Finding a Maximum Non-k-linked Graph
A graph with at least 2k vertices is said to be k-linked if for any ordered k-tuples (s1, . . . , sk) and (t1, . . . , tk) of 2k distinct vertices, there exist pairwise vertex-disjoint paths P1, . . . , Pk such that Pi connects si and ti for i = 1, . . . , k. For a given graph G, we consider the problem of finding a maximum induced subgraph of G that is not k-linked. This problem is a common ge...
متن کامل