Continuum of All-Pair Shortest-Path to All-Path via Random Walk
نویسندگان
چکیده
A method is proposed to compute the continuum of paths, from shortest paths to all random paths between all pairs of nodes at once in a unified way. The analysis is based on treating the network as a random walk with an additional absorbing state named evaporating state reachable with nonzero probability from any state (so called “evaporating random walk”). The probability of avoiding absorption is tuned by a single parameter varying between 0 and 1, with lower values favoring shorter paths. A computational example is used to illustrate the method.
منابع مشابه
From Shortest - path to All - path : The Routing Continuum Theory and its applications ( Supplementary Materials )
This documents provides numerical illustration results obtained by applying the routing continuum theory in two synthetic networks and a real network topology. Moreover, besides the generalizations of the mixed L1and L2-norm network flow optimization problem discussed in the main file, in this document, we discuss one more application in analyzing network robustness, by introducing the generali...
متن کاملTwo optimal algorithms for finding bi-directional shortest path design problem in a block layout
In this paper, Shortest Path Design Problem (SPDP) in which the path is incident to all cells is considered. The bi-directional path is one of the known types of configuration of networks for Automated Guided Vehi-cles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Pro-gramming (ILP) is determined. The objective functions of both algorithms are t...
متن کاملSolving the all-pair shortest path query problem on interval and circular-arc graphs
In this paper, we study the following all-pair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed eeciently (both sequentially and in parallel). We show that, after sorting the input intervals by their endpo...
متن کاملA Random Walk with Exponential Travel Times
Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
متن کاملA Shortest Path Similarity Matrix based Spectral Clustering
This paper proposed a new spectral graph clustering model by casting the non-categorical spatial data sets into an undirected graph. Decomposition of the graph to Delaunay graph has been done for computational efficiency. All pair shortest path based model has been adapted for the creation of the underlying Laplacian matrix of the graph. The similarity among the nodes of the graph is measured b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013