An efficient distributed depth-first-search algorithm

doi:10.1016/0020-0190(89)90041-0

Information Processing Letters

Volume 32, Issue 4, 1 September 1989, Pages 183-186

https://doi.org/10.1016/0020-0190(89)90041-0 Get rights and content

Abstract

The sequential depth-first-search algorithm, distributed over processor nodes of a graph, yields a distributed depth-first-search algorithm that uses exactly 2|V| messages and 2|V| units of time.

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Inform. Process. Lett.
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Graph traversal techniques and the maximum flow problem in distributed computation
IEEE Trans. Software Eng.
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There are more references available in the full text version of this article.

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A linear time algorithm for finding depth-first spanning trees on trapezoid graphs
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Let G be a connected graph of n vertices and m edges. The problem of finding a depth-first spanning tree of G is to find a subgraph of G connecting the n vertices with n − 1 edges by depth-first search. In this paper, we propose an O(n) time algorithm for solving this problem on trapezoid graphs. Our algorithm can also find depth-first spanning trees of permutation graphs in linear time, improving the recent algorithm on permutation graphs which takes O(n log log n) time.
On the impact of sense of direction on message complexity
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In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, Depth First Traversal, Election, and Spanning Tree Construction. In systems with n nodes and e communication links, the solution for the Depth First Traversal and the Broadcast problems require $Ω(e)$ messages with arbitrary labelings; we show that, with any sense of direction, they can be solved exchanging only Θ(n) messages, even if the system is anonymous. The problems of Election and of Spanning Tree Construction require $Ω(e + n log n)$ messages with arbitrary labelings; on the other hand, we show that they can be solved with Θ(n) messages with any sense of direction. The results presented here completely explain and generalize the existing results which now follow as corollaries for specific labelings.
Distributed algorithms for depth-first search
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We present distributed algorithms for constructing a depth-first search tree for a communication network which are more efficient than previous methods. Our algorithms require 2|V| − 2 messages and units of time in the worst case, where |V| is the number of sites in the network, and as little as |V| messages and time units in the best case. The actual number of messages and time units depends on the network topology and possibly on the routing chosen. We can interpret this to mean that the number of messages and time units is |V|(1 + r) in the worst case, where 0 ⩽ r < 1 and the value of r depends on the topology and the routing. In a best case for the simplest algorithm, for example when the underlying network has a ring topology, r = 0 and our basic algorithm requires |V| messages and time units, regardless of routing. We extend the basic algorithm to achieve the same best case bound for other topologies. The worst case bound, which has $r = 1 − 2 |V|$ , applies if the network topology is a tree. The improvement over the best of previous algorithms is achieved by dynamic backtracking, with a minor increase in message length.

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An efficient distributed depth-first-search algorithm

Abstract

Inform. Process. Lett.

Inform. Process. Lett.

Inform. Process. Lett.

Graph traversal techniques and the maximum flow problem in distributed computation

IEEE Trans. Software Eng.