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COMPLEXITY OF GRAPH POLYNOMIALS

Steven D. Noble

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0013
Subject:
Mathematics, Probability / Statistics

This chapter examines the complexity of evaluating graph polynomials, related to the Tutte polynomial, for various classes of matroids. It begins with a short introduction to matroids, complexity, ... More


The Winner Determination Problem

Daniel Lehmann, Rudolf Müller, and Tuomas Sandholm

in Combinatorial Auctions

Published in print:
2005
Published Online:
August 2013
ISBN:
9780262033428
eISBN:
9780262302920
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033428.003.0013
Subject:
Society and Culture, Technology and Society

This chapter defines and formulates a combinatorial optimization problem, called the winner determination problem, and examines its complexity properties. A range of alternative mathematical ... More


Seymour's Decomposition Theorem

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0014
Subject:
Mathematics, Educational Mathematics

The excluded-minor theorem provides one characterization of the class of regular matroids. This chapter presents a different characterization of this class: a decomposition theorem for members of the ... More


Computing the residual Galois representations

Bas Edixhoven

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0014
Subject:
Mathematics, Number Theory

This chapter proves the main result on the computation of Galois representations. It provides a detailed description of the algorithm and a rigorous proof of the complexity. It first combines the ... More


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