//Dijiskra algorithm #include<iostream> #include<memory> #include<algorithm> using namespace std; const int MAX = 1005; const int INF = 0x3f3f3f3f; int n, m; int d[MAX]; bool v[MAX]; int edge[MAX][MAX]; void Dijiskra(int start) { //initial memset(v, false, sizeof(v));...
Shortest pathsGiven a simple connected unweighted undirected graph G = (V (G), E(G)) with ∣V (G)∣ = n and ∣E(G)∣ = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n² log n). This bound is an...
We present an algorithm, APD, that solves the distance version of the all-pairs-shortest-path problem for undirected, unweighted n-vertex graphs in time O(M(n) log n), where M(n) denotes the time necessary to multiply two n x n matrices of small integers (which is currently known to...
When I was developing the algorithm, I found some interesting points about the algorithm that I could explore further to find more ways to optimize the algorithm.Node with A Single NeighborWhen a node only has a sinlge neighbore, that neighbor is the shortest path to all other nodes....
approximatedistanceoraclesinexpected timeifthegraphisunweighted.Oneofthenewideasusedintheimprovedalgorithmalsoleadstothe firstlineartimealgorithmforcomputinganoptimalsize-spannerofanunweightedgraph. 1Introduction Theall-pairsshortestpathsproblemisoneofthemostfundamentalalgorithmicgraphproblem.Every computerscientistis...
unweightedShortestPaths =newUnweightedShortestPath(theGraph); id = Indexer.getAndUpdateIndexer(theGraph, LAYOUT_INDEX_KEY);// This is practically fast, but it would be the best if we have an// implementation of All Pairs Shortest Paths(APSP) algorithm.diameter = getDiameter(n, id);intwidth...
which require numerous expensive shortest distance calculations. We propose batched algorithm execution to run multiple distance and centrality computations at the same time and let them share common graph and data accesses. Batched execution amortizes the high cost of random memory accesses and present...
Let G = (V, E) be a directed graph and let P be a shortest path from s to t in G. In the replacement paths problem we are required to find, for every edge e on P, a shortest path from s to t in G that avoids e. We present the first non-trivial algorithm for computing ...
In this paper,based on the adjacency matrix of the network and its powers,the formulas are derived for theshortest path and the average path length,and an effective algorithm is presented.Furthermore,an example is providedto demonstrate the proposed method.LIU Chun-PingLIU Yu-RongHE Da-RenZHU...
Non-Crossing Shortest Paths in Undirected Unweighted Planar Graphs in Linear Time2022, Brown University. All rights reserved.Given a set of terminal pairs on the external face of an undirected unweighted planar graph, we give a linear-time algorithm for computing the union of non-crossing shortest...