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EdgeSelection Heuristics for Computing Tutte Polynomials
, 2009
"... The Tutte polynomial of a graph, also known as the partition function of the qstate Potts model, is a 2variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and ..."
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The Tutte polynomial of a graph, also known as the partition function of the qstate Potts model, is a 2variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial as partial evaluations, and various numerical invariants such as the number of spanning trees as complete evaluations. We have developed the most efficient algorithm todate for computing the Tutte polynomial of a graph. An important component of the algorithm affecting efficiency is the choice of edge to work on at each stage in the computation. In this paper, we present and discuss two edgeselection heuristics which (respectively) give good performance on sparse and dense graphs. We also present experimental data comparing these heuristics against a range of others to demonstrate their effectiveness.
A new edge selection heuristic for computing the Tutte polynomial of an undirected graph.
"... Abstract. We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the Tutte polynomial of the truncated icosahedron graph us ..."
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Abstract. We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the Tutte polynomial of the truncated icosahedron graph using our Maple implementation in under 4 minutes on a single CPU. This compares with a recent result of Haggard, Pearce and Royle whose special purpose C++ software took one week on 150 computers. Résumé. Nous présentons deux nouvelles heuristiques pour le calcul du polynôme de Tutte de graphes de faible densité, basées sur les principes de sélection d’arêtes et d’arrangement linéaire de sommets, et qui permettent de traiter des graphes de bien plus grande tailles que les méthodes existantes. Par exemple, en utilisant notre implémentation en Maple, nous pouvons calculer le polynôme de Tutte de l’isocahédron tronqué en moins de 4 minutes sur un ordinateur à processeur unique, alors qu’un programme adhoc récent de Haggard, Pearce et Royle, utilisant 150 ordinateurs, a nécessité une semaine de calcul pour obtenir le même résultat.
Chapter 25 Using Secure Auctions to Build a Distributed Metascheduler for the Grid
"... The previous chapter introduced a number of different techniques for establishing trustworthy Grid resource or service auctions. These protocols permit new architectures that are community or peer oriented to be developed without compromising the integrity of the resource or service allocations. In ..."
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The previous chapter introduced a number of different techniques for establishing trustworthy Grid resource or service auctions. These protocols permit new architectures that are community or peer oriented to be developed without compromising the integrity of the resource or service allocations. In this chapter we will look at an architecture that
Tutte Polynomial of MultiBridge Graphs
 COMPUTER SCIENCE JOURNAL OF MOLDOVA, VOL.21, NO.2(62)
, 2013
"... In this paper, using a wellknown recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multibridge graph and some 2−tree graphs. Further, several recursive formulae for other graphs such as the fan and the wheel graphs are also discu ..."
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In this paper, using a wellknown recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multibridge graph and some 2−tree graphs. Further, several recursive formulae for other graphs such as the fan and the wheel graphs are also discussed.
Visualising the Tutte Polynomial Computation
"... Abstract—The Tutte polynomial is an important concept in graph theory which captures many important properties of graphs (e.g. chromatic number, number of spanning trees etc). It also provides a normalised representation that can be used as an equivalence relation on graphs and has applications in d ..."
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Abstract—The Tutte polynomial is an important concept in graph theory which captures many important properties of graphs (e.g. chromatic number, number of spanning trees etc). It also provides a normalised representation that can be used as an equivalence relation on graphs and has applications in diverse areas such microbiology and physics. A highly efficient algorithm for computing Tutte polynomials has been elsewhere developed by Haggard and Pearce. This relies on various optimisations and heuristics to improve performance; however, understanding the effect of a particular heuristic remains challenging, since the computation trees involved are very large. Therefore, we have constructed a visualisation of the computation in order to study the effect of various heuristics on the algorithms ’ operation. I.
A Complete Bibliography of ACM Transactions on Graphics
, 2013
"... Version 1.99 Title word crossreference ..."