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

Li-Hsuan Chen, Felix Reidl, Peter Rossmanith, Fernando Sánchez Villaamil
2018 Algorithms  
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 treeor 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 1) n for DOMINATING SET for any > 0. This
more » ... rmalizes 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 d O(d 2 ) · n and uses space O(d 3 log d + d log n) and a hybrid of branching and dynamic programming that achieves a running time of O(3 d log d · n) while using O(2 d d log d + d log n) space.
doi:10.3390/a11070098 fatcat:4diwb3o3fzfn7jz6joixddfbry