TY - JOUR

T1 - Efficient computation of the characteristic polynomial of a threshold graph

AU - Fürer, Martin

N1 - Funding Information:
This work was supported by the National Science Foundation [NSF Grant CCF-1320814 ].
Publisher Copyright:
© 2016

PY - 2017/1/2

Y1 - 2017/1/2

N2 - An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chvátal and Hammer, as well as by Henderson and Zalcstein in 1977. A threshold graph is obtained from a one vertex graph by repeatedly adding either an isolated vertex or a dominating vertex, which is a vertex adjacent to all the other vertices. Threshold graphs are special kinds of cographs, which themselves are special kinds of graphs of clique-width 2. We obtain a running time of O(nlog2n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time. We improve the running time drastically in the case where there is a small number of alternations between 0's and 1's in the sequence defining a threshold graph.

AB - An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chvátal and Hammer, as well as by Henderson and Zalcstein in 1977. A threshold graph is obtained from a one vertex graph by repeatedly adding either an isolated vertex or a dominating vertex, which is a vertex adjacent to all the other vertices. Threshold graphs are special kinds of cographs, which themselves are special kinds of graphs of clique-width 2. We obtain a running time of O(nlog2n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time. We improve the running time drastically in the case where there is a small number of alternations between 0's and 1's in the sequence defining a threshold graph.

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U2 - 10.1016/j.tcs.2016.07.013

DO - 10.1016/j.tcs.2016.07.013

M3 - Article

AN - SCOPUS:84979650049

VL - 657

SP - 3

EP - 10

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -