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• W2783306705 abstract "Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the decomposition’s width. Following the work of Allender et al. [5], we investigate whether this space complexity explosion is unavoidable. Using the idea of reparameterization of Cai and Juedes [18], we prove that the question is closely related to a conjecture that the L ongest C ommon S ubsequence problem parameterized by the number of input strings does not admit an algorithm that simultaneously uses XP time and FPT space. Moreover, we extend the complexity landscape sketched for pathwidth and treewidth by Allender et al. by considering the parameter tree-depth . We prove that computations on tree-depth decompositions correspond to a model of non-deterministic machines that work in polynomial time and logarithmic space, with access to an auxiliary stack of maximum height equal to the decomposition’s depth. Together with the results of Allender et al., this describes a hierarchy of complexity classes for polynomial-time non-deterministic machines with different restrictions on the access to working space, which mirrors the classic relations between treewidth, pathwidth, and tree-depth." @default.
• W2783306705 created "2018-01-26" @default.
• W2783306705 creator A5000479623 @default.
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• W2783306705 date "2017-12-31" @default.
• W2783306705 modified "2023-10-08" @default.
• W2783306705 title "On Space Efficiency of Algorithms Working on Structural Decompositions of Graphs" @default.
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• W2783306705 doi "https://doi.org/10.1145/3154856" @default.
• W2783306705 hasPublicationYear "2017" @default.
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