Connectivity algorithm with depth first search (DFS) on simple graphs

Depth First Search in Graphs

On a Simple Depth-First Search Strategy for Exploring Unknown Graphs

We present a simple depth-rst search strategy for exploring (constructing) an unknown strongly connected graph G with m edges and n vertices by traversing at most min(mn; dn 2 + m) edges. Here, d is the minimum number of edges needed to add to G to make it Eulerian. This parameter d is known as the deeciency of a graph and was introduced by Kutten Kut88]. It was conjectured that graphs with low...

An Efficient Distributed Depth-First-Search Algorithm

Consider a communication network. Our goal is to equip the set of processors in the network with a control algorithm that will allow a processor in the network to effect a depth-first traversal through the graph underlying the network, using messages. The output of the algorithm is a depthfirst-search (DFS) tree of the graph underlying the network, kept in a distributed fashion, i.e., at the en...

Yet Another Distributed Depth-First-Search Algorithm

In a recent paper [1], Awerbuch suggests a distributed depth-first-search (DDFS) algorithm that improves the time complexity of the previous DDFS algorithm of Cheung [2]. The communication cost of the algorithm of [I] is 41 E I messages and the time complexity is less than 41V 1, where E is the set of undirected links and V is the set of nodes of the communication network. This is compared to 2...

I/O-Efficient Strong Connectivity and Depth-First Search for Directed Planar Graphs

We present the first I/O-efficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simple-path 3 -separator, and computing a depth-first spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B) logM/B(N/B)) is the number of I/Os required to sort ...