A note on k-shortest paths problem

نویسندگان

  • Nick Gravin
  • Ning Chen
چکیده

It is well-known that in a directed graph, if deleting any edge will not affect the shortest distance between two specific vertices s and t, then there are two edge-disjoint paths from s to t and both of them are shortest paths. In this paper, we generalize this to shortest k edge-disjoint s-t paths for any positive integer k.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS

Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

متن کامل

A New Algorithm for the Discrete Shortest Path Problem in a Network Based on Ideal Fuzzy Sets

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for ...

متن کامل

The Directed Disjoint Shortest Paths Problem

In the k disjoint shortest paths problem (k-DSPP), we are given a graph and its vertex pairs (s1, t1), . . . , (sk, tk), and the objective is to find k pairwise disjoint paths P1, . . . , Pk such that each path Pi is a shortest path from si to ti, if they exist. If the length of each edge is equal to zero, then this problem amounts to the disjoint paths problem, which is one of the well-studied...

متن کامل

A summary of shortest-paths results

This note attempts to summarize the best of the currently existing theoretical results on the single-source shortest paths problem for graphs with non-negative edge weights. The main purpose of this note is to make available the statements of all of these results, as well as the building blocks they use, together in one document. We also note some new theoretical implications of a recent result...

متن کامل

Implementations and empirical comparison of K shortest loopless path algorithms

The first work on the network optimisation problem of rankingK shortest paths, K ∈ IN, appeared in 1959, more or less simultaneously with the first papers on the shortest path problem. Since then the particular problem (when K = 1) has merited much more attention than its generalisation. Nevertheless, several titles are included on the very complete bibliography about theK shortest paths proble...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Journal of Graph Theory

دوره 67  شماره 

صفحات  -

تاریخ انتشار 2011