SIAM Journal on Discrete Mathematics 

About: SIAM Journal on Discrete Mathematics is an academic journal published by Society for Industrial and Applied Mathematics. The journal publishes majorly in the area(s): Mathematics & Combinatorics. It has an ISSN identifier of 0895-4801. Over the lifetime, 2805 publications have been published receiving 72297 citations. The journal is also known as: Discrete mathematics & Journal on discrete mathematics.

A hierarchy of relaxation between the continuous and convex hull representations

Abstract: In this paper a reformulation technique is presented that takes a given linear zero-one programming problem, converts it into a zero-one polynomial programming problem, and then relinearizes it into an extended linear program. It is shown that the strength of the resulting reformulation depends on the degree of the terms used to produce the polynomial program at the intermediate step of this method. In fact, as this degree varies from one up to the number of variables in the problem, a hierarchy of sharper representations is obtained with the final relaxation representing the convex hull of feasible solutions. The reformulation technique readily extends to produce a similar hierarchy of linear relaxations for zero-one polynomial programming problems. A characterization of the convex hull in the original variable space is also available through a projection process. The structure of this convex hull characterization (or its other relaxations) can be exploited to generate strong or facetial valid inequaliti...

Singularity analysis of generating functions

Abstract: This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic expans...

Labelling graphs with a condition at distance 2

Abstract: Given a simple graph $G = ( V,E )$ and a positive number d, an $L_d ( 2,1 )$-labelling of G is a function $f:V ( G ) \to [ 0,\infty )$ such that whenever $x,y \in V$ are adjacent, $| f ( x ) - f ( ...

The probabilistic communication complexity of set intersection

Abstract: It is shown that, for inputs of length n, the probabilistic (bounded error) communication complexity of set intersection is $\Theta ( n )$. Since set intersection can be recognized nondeterministic...

A mathematical for periodic scheduling problems

Abstract: A mathematical model is proposed for scheduling activities of periodic type. First a model is proposed for scheduling periodic events with particular time constraints. This problem, which could be considered the extension to periodic phenomena of ordinary scheduling with precedence constraints, is shown to be NP-complete. An algorithm for it of implicit enumeration type is designed based on network flow results, and its average complexity is discussed. Some extensions of the model are considered. The results of this first part serve as a basis in modelling periodic activities using resources. Several cases are considered. Finally some applications are presented for which the proposed model can be a useful tool.