Finding k Disjoint Paths in a Directed Planar Graph
نویسندگان
چکیده
منابع مشابه
FINDING k PARTIALLY DISJOINT PATHS IN A DIRECTED PLANAR GRAPH
The partially disjoint paths problem is: given: a directed graph, vertices r1, s1, . . . , rk, sk, and a set F of pairs {i, j} from {1, . . . , k}, find: for each i = 1, . . . , k a directed ri − si path Pi such that if {i, j} ∈ F then Pi and Pj are disjoint. We show that for fixed k, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is sol...
متن کاملFinding k Disjoint Paths in a Directed Planar Graph
We show that for each fixed k, the problem of finding k pairwise vertex-disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time.
متن کاملFinding Disjoint Paths on Directed Acyclic Graphs
Given k + 1 pairs of vertices (s1, s2), (u1, v1), . . . , (uk, vk) of a directed acyclic graph, we show that a modified version of a data structure of Suurballe and Tarjan can output, for each pair (ul, vl) with 1 ≤ l ≤ k, a tuple (s1, t1, s2, t2) with {t1, t2} = {ul, vl} in constant time such that there are two disjoint paths p1, from s1 to t1, and p2, from s2 to t2, if such a tuple exists. Di...
متن کاملA Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph
We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein’s algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen’s algorithm [19] and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-ar...
متن کاملDisjoint Paths in Planar Graphs
ACKNOWLEDGEMENTS My thanks first to my advisor, Xingxing Yu. He has helped me find my strengths, and directed me toward questions which truly intrigue me. He kept me moving forward in moments of frustration, set high expectations, and provided support for me to meet them. their service on my thesis committee. I would also like to thank Robin Thomas and the rest of the faculty at Georgia Tech fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1994
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539792224061