Abstract
Following the recent trends of designing space efficient algorithms for fundamental algorithmic graph problems, we present several time-space tradeoffs for performing maximum cardinality search (MCS), stack breadth first search, and queue breadth first search on a given input graph. As applications of these results, we also provide space-efficient implementations for testing if a given undirected graph is chordal, reporting an independent set, and a proper coloring of a given chordal graph among others. Finally, we also show how two other seemingly different graph problems and their algorithms have surprising connection with MCS with respect to designing space efficient algorithms.
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Notes
We use \(\lg \) to denote logarithm to the base 2.
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Some of these results were announced in preliminary form in the proceedings of 23rd International Computing and Combinatorics Conference (COCOON 2017), Springer LNCS volume 10392, pages 87–98 (Chakraborty and Satti 2017). Part of this work was done while the first author was affiliated to The Institute Mathematical Sciences, HBNI, India.
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Chakraborty, S., Satti, S.R. Space-efficient algorithms for maximum cardinality search, its applications, and variants of BFS. J Comb Optim 37, 465–481 (2019). https://doi.org/10.1007/s10878-018-0270-1
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DOI: https://doi.org/10.1007/s10878-018-0270-1