TY - GEN

T1 - Efficient computation of the characteristic polynomial of a tree and related tasks

AU - Fürer, Martin

PY - 2009

Y1 - 2009

N2 - An O(n log2 n) algorithm is presented to compute the characteristic polynomial of a tree on n vertices improving on the previously best quadratic time. With the same running time, the algorithm can be generalized in two directions. The algoritm is a counting algorithm, and the same ideas can be used to count other objects. For example, one can count the number of independent sets of all possible sizes simultaneously with the same running time. These counting algorithms not only work for trees, but can be extended to arbitrary graphs of bounded tree-width.

AB - An O(n log2 n) algorithm is presented to compute the characteristic polynomial of a tree on n vertices improving on the previously best quadratic time. With the same running time, the algorithm can be generalized in two directions. The algoritm is a counting algorithm, and the same ideas can be used to count other objects. For example, one can count the number of independent sets of all possible sizes simultaneously with the same running time. These counting algorithms not only work for trees, but can be extended to arbitrary graphs of bounded tree-width.

UR - http://www.scopus.com/inward/record.url?scp=70350397063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350397063&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04128-0_2

DO - 10.1007/978-3-642-04128-0_2

M3 - Conference contribution

AN - SCOPUS:70350397063

SN - 3642041272

SN - 9783642041273

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 11

EP - 22

BT - Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings

T2 - 17th Annual European Symposium on Algorithms, ESA 2009

Y2 - 7 September 2009 through 9 September 2009

ER -