Multiple Source Dual Fault Tolerant BFS Trees
Manoj Gupta, Shahbaz Khan

TL;DR
This paper introduces a simplified algorithm for constructing dual fault-tolerant BFS trees in directed graphs with multiple sources, extending previous work to vertex failures and improving analysis simplicity.
Contribution
It presents a simpler, more versatile algorithm for dual FT-BFS and FT-MBFS problems, applicable to directed graphs and vertex failures, matching known lower bounds.
Findings
Algorithm works for directed graphs and vertex failures.
Achieves space complexity matching lower bounds.
Provides a dual fault-tolerant spanner with +2 stretch and size O(n^{7/8}).
Abstract
Let be a graph with vertices and edges, with a designated set of sources . The fault tolerant subgraph for any graph problem maintains a sparse subgraph of , such that for any set of failures, the solution for the graph problem on is maintained in . We address the problem of maintaining a fault tolerant subgraph for Breath First Search tree (BFS) of the graph from a single source (referred as FT-BFS) or multiple sources (referred as FT-MBFS). The problem of FT-BFS was first studied by Parter and Peleg [ESA13]. They designed an algorithm to compute FT-BFS subgraph of size . Further, they showed how their algorithm can be easily extended to FT-MBFS requiring space. They also presented matching lower bounds for these results. The…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Optimization and Search Problems
