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Article

Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming

1
AROBOT Innovation, Taiwan
2
Royal Holloway, University of London, TW20 0EX, UK
3
Department of Computer Science, RWTH Aachen University, 52062 Aachen, Germany
*
Author to whom correspondence should be addressed.
Algorithms 2018, 11(7), 98; https://doi.org/10.3390/a11070098
Received: 31 March 2018 / Revised: 27 June 2018 / Accepted: 28 June 2018 / Published: 1 July 2018
(This article belongs to the Special Issue Algorithms for Hard Problems: Approximation and Parameterization)
Treedepth is a well-established width measure which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded tree- or pathwidth, we are interested in the algorithmic utility of this additional structure. On the negative side, we show with a novel approach that the space consumption of any (single-pass) dynamic programming algorithm on treedepth decompositions of depth d cannot be bounded by (2ϵ)d·logO(1)n for Vertex Cover, (3ϵ)d·logO(1)n for 3-Coloring and (3ϵ)d·logO(1)n for Dominating Set for any ϵ>0. This formalizes the common intuition that dynamic programming algorithms on graph decompositions necessarily consume a lot of space and complements known results of the time-complexity of problems restricted to low-treewidth classes. We then show that treedepth lends itself to the design of branching algorithms. Specifically, we design two novel algorithms for Dominating Set on graphs of treedepth d: A pure branching algorithm that runs in time dO(d2)·n and uses space O(d3logd+dlogn) and a hybrid of branching and dynamic programming that achieves a running time of O(3dlogd·n) while using O(2ddlogd+dlogn) space. View Full-Text
Keywords: treewidth; treedepth; dynamic programming; branching algorithm; space lower bound treewidth; treedepth; dynamic programming; branching algorithm; space lower bound
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MDPI and ACS Style

Chen, L.-H.; Reidl, F.; Rossmanith, P.; Sánchez Villaamil, F. Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming. Algorithms 2018, 11, 98. https://doi.org/10.3390/a11070098

AMA Style

Chen L-H, Reidl F, Rossmanith P, Sánchez Villaamil F. Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming. Algorithms. 2018; 11(7):98. https://doi.org/10.3390/a11070098

Chicago/Turabian Style

Chen, Li-Hsuan, Felix Reidl, Peter Rossmanith, and Fernando Sánchez Villaamil. 2018. "Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming" Algorithms 11, no. 7: 98. https://doi.org/10.3390/a11070098

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