This paper addresses memory requirement issues arising in implementations of algorithms on graphs of bounded treewidth. Such dynamic programming algorithms require a large data table for each vertex of a tree-decomposition T of the input graph. We give a linear-time algorithm that finds the traversal order of T minimizing the number of tables stored simultaneously. We show that this minimum value is lower-bounded by the pathwidth of T plus one, and upper bounded by twice the pathwidth of T plus one. We also give a linear-time algorithm finding the depth-first traversal order minimizing the sum of the sizes of tables stored simultaneously.
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