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Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth by Bergougnoux, Benjamin; Chekan, Vera; Ganian, Robert; Kanté, Mamadou Moustapha; Mnich, Matthias; Oum, Sang-il; Pilipczuk, Michał; van Leeuwen, Erik Jan is a scholarly article available to read on EtoBox.

What is Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth about?

Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition's width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms which achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width alone. Motivated by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth (sd). Here, sd is a bounded-depth analogue of cliquewidth, in the same way as td is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. Pr

Author

Bergougnoux, Benjamin; Chekan, Vera; Ganian, Robert; Kanté, Mamadou Moustapha; Mnich, Matthias; Oum, Sang-il; Pilipczuk, Michał; van Leeuwen, Erik Jan

Published

2023

Language

EN