# A GENERIC APPROACH FOR SPARSE PATH PROBLEMS

### Marc Pouly

#### Abstract

This paper shows how sparse path problems can be solved by tree-decomposition techniques. We analyse the properties of closure matrices and prove that they satisfy the axioms of a valuation algebra, which is known to be sufficient for the application of generic tree-decomposition methods. Given a sparse path problem where only a subset of queries are required, we continually compute path weights of smaller graph regions and deduce the total paths from these results. The decisive complexity factor is no more the total number of graph nodes but the induced treewidth of the path problem.

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#### Paper Citation

#### in Harvard Style

Pouly M. (2010). **A GENERIC APPROACH FOR SPARSE PATH PROBLEMS** . In *Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-674-021-4, pages 197-202. DOI: 10.5220/0002702701970202

#### in Bibtex Style

@conference{icaart10,

author={Marc Pouly},

title={A GENERIC APPROACH FOR SPARSE PATH PROBLEMS},

booktitle={Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2010},

pages={197-202},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002702701970202},

isbn={978-989-674-021-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - A GENERIC APPROACH FOR SPARSE PATH PROBLEMS

SN - 978-989-674-021-4

AU - Pouly M.

PY - 2010

SP - 197

EP - 202

DO - 10.5220/0002702701970202