Time-Space Tradeoffs for Dynamic Programming Algorithms in Trees and Bounded Treewidth Graphs

The well-known Courcelle's theorem states that many graph properties (that are expressible in monadic second order logic) can be solved in linear time on graphs of bounded treewidth. Logspace versions of this using automata theoretic framework are also known. In this paper, we develop an alternate methodology using the standard table-based dynamic programming approach to give a space efficient version of Courcelle's theorem. We assume that the given graph and its tree decomposition are given in a read-only memory. Our algorithms use the recently developed stack-compression machinery and the classical framework of Borie et al. to develop time-space tradeoffs for dynamic programming algorithms that use O(p log(p)n) variables where 2 <= p <= n is a parameter. En route we also generalize the stack compression framework to a broader class of algorithms, which we believe can be of independent interest.