Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space Saving by Dynamic Algebraization   Dynamic programming is widely used for exact computations based on tree
decompositions of graphs. However, the space complexity is usually exponential
in the treewidth. We study the problem of designing efficient dynamic
programming algorithm based on tree decompositions in polynomial space. We show
how to construct a tree decomposition and extend the algebraic techniques of
Lokshtanov and Nederlof such that the dynamic programming algorithm runs in
time $O^*(2^h)$, where $h$ is the maximum number of vertices in the union of
bags on the root to leaf paths on a given tree decomposition, which is a
parameter closely related to the tree-depth of a graph. We apply our algorithm
to the problem of counting perfect matchings on grids and show that it
outperforms other polynomial-space solutions. We also apply the algorithm to
other set covering and partitioning problems.

6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci