Showing papers in "Discrete Applied Mathematics in 2009"

TL;DR: This work considers models of the spread of disease or opinion through social networks, represented as graphs, called an irreversible k-threshold process, where a vertex enters state 1 if at least k of its neighbors are in state 1, andwhere a vertex never leaves state 1 once it is in it.

TL;DR: Some exact expressions for the first and second Zagreb indices of graph operations containing the Cartesian product, composition, join, disjunction and symmetric difference of graphs will be presented.

TL;DR: It has been proven that, among all trees, the star tree, S"n, has the maximal ABC value, and chemical trees with extremal ABC values are found.

TL;DR: This paper provides a survey of recent results addressing the clique-width of graphs in a certain class of graphs and shows that for many classes of graphs, this parameter has been proved to be unbounded.

TL;DR: A polytope is defined associated to the problem and a partial linear description whose integral points are the incidence vectors of a layout is presented, and a new lower bound is proposed for the problem by optimizing a linear program over the partial description given.

TL;DR: This paper presents QCR, a general method to reformulate (QP) into an equivalent 0-1 program with a convex quadratic objective function, and shows that QCR is optimal in a certain sense.

TL;DR: A new class of algorithms to estimate the cardinality of very large multisets using constant memory and doing only one pass on the data is introduced here, based on order statistics rather than on bit patterns in binary representations of numbers.

TL;DR: This paper compares two cutting-plane algorithms to compute the same lower bound on the optimal value of the 0-1 reformulation of the multicommodity capacitated network design problem, and develops a column-and-row generation approach that is competitive with the approach relying on residual capacity inequalities.

TL;DR: This paper introduces four new operations on graphs and study the Wiener indices of the resulting graphs.

TL;DR: The spectrum of the binary hypertree T"m (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct.

TL;DR: A large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual by considering a (generalized) augmented Lagrangian of the primal master problem.

TL;DR: The results of a query expressed by a monadic second-order formula on a tree, on a graph or on a relational structure of tree-width at most k, can be enumerated with a delay between two outputs proportional to the size of the next output using a preprocessing that takes time O([email protected]?log(n), where n is the number of vertices or elements.

TL;DR: Kirchhoff index formulae of these composite graphs are given and show the join, corona and cluster of graphs G"1 and G"2, respectively.

TL;DR: This work provides first-time fixed-parameter tractability results for planar graphs, bounded-degree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth.

TL;DR: The spectrum of the (normalized) graph Laplacian is presented as a systematic tool for the investigation of networks, and basic properties of eigenvalues and eigenfunctions are described.

TL;DR: The notion of the transition graph T(G) whose vertices are maximal cliques of G and arcs are transitions between cliques is introduced and it is shown that under some specific numbering, the transition graphs has a hamiltonian path for chordal and comparability graphs.

TL;DR: All extremal unicyclic graphs having the largest signless Laplacian spectral radius are obtained in the sets of all unicyCLic graphs of order n with a specified number of leaves or maximum degree or independence number or matching number.

TL;DR: This paper gives an exact formula of minimum wirelength of hypercube layout into grids and thereby it solves completely the wirelength problem of hypercubes into grids.

TL;DR: In this paper a covering type of model for the discrete ordered median problem is presented, which reduces the number of binary variables tremendously, and several variable fixing strategies are identified.

TL;DR: It is proved the asymptotically sharp upper bound D^'(G)@?14nd(n-d)^2+O(n^7^/^2) for graphs of order n and diameter d is correct.

TL;DR: This paper presents a Mixed 0-1 Integer and Linear Programming (MILP) approach that can identify LAD patterns that are optimal with respect to various previously studied and new pattern selection preferences and demonstrates the utility of the MILP-based pattern generation.

TL;DR: This paper shows that @c"r"2(P(n,2))=@?4n5@?+@a, where @a=0 for n=0,3,4,9mod10 and @a-1 for n =1,2,5,6,7,8mod10, and shows the answer to the question is put forward.

TL;DR: The aim is to prove the first part of the conjecture for all the finite non-abelian simple groups H, and to show that the graph isomorphism @C"[email protected][email protected]"H implies [email-protected]?H.

TL;DR: This work presents a new constraint-based approach to metabolic pathway analysis which uses an outer description of the flux cone, based on sets of non-negativity constraints, which satisfies a simplicity condition similar to the one that holds for elementary flux modes.

TL;DR: Here it is shown that the use of submodular flows is actually avoidable and even a common generalization of the two rooted k-connection problems reduces to matroid intersection and the approach is based on a new matroid construction extending what Whiteley calls count matroids.

TL;DR: The proposed question: Is @c"r"2(P(n,3))=n for all n>=7 where n is not divisible by 3?

TL;DR: In this paper, a review of column generation formulations for the Routing and Wavelength Assignment (rwa) problem with the objective of minimizing the blocking rate is presented, together with a comparison of the different formulations with respect to the quality of their continuous relaxation bounds and their computing solution ease.

TL;DR: The results imply limitations on this kind of reduction and establish, for the first time, that it cannot be used in general to minimise arbitrary submodular functions.

TL;DR: A generalization of the Blocking Job Shop problem which takes into account transfer operations between machines and sequence-dependent setup times is studied, and a neighborhood for local search is developed, based on which a tabu search algorithm is devised.

TL;DR: This paper improves and extends previous results in three ways: the algorithms proposed work in one stage, which saves time for testing, the test complexity is lower than previous results, and the number of elements which need to be tested is sufficiently large.