The interleaved multichromatic number of a graph

For $k\ge 1$, we consider interleaved $k$-tuple colorings of the nodes of a graph, that is, assignments of $k$ distinct natural numbers to each node in such a way that nodes that are connected by an edge receive numbers that are strictly alternating between them with respect to the relation $<$. If it takes at least $\chi_{int}^k(G)$ distinct numbers to provide graph $G$ with such a coloring, then the interleaved multichromatic number of $G$ is $\chi_{int}^*(G)=\inf_{k\ge 1}\chi_{int}^k(G)/k$ and is known to be given by a function of the simple cycles of $G$ under acyclic orientations if $G$ is connected [1]. This paper contains a new proof of this result. Unlike the original proof, the new proof makes no assumptions on the connectedness of $G$, nor does it resort to the possible applications of interleaved $k$-tuple colorings and their properties

A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs

Probabilistic heuristics for disseminating information in networks

We study the problem of disseminating a piece of information through all the nodes of a network, given that it is known originally only to a single node. In the absence of any structural knowledge on the network other than the nodes' neighborhoods, this problem is traditionally solved by flooding all the network's edges. We analyze a recently introduced probabilistic algorithm for flooding and give an alternative probabilistic heuristic that can lead to some cost-effective improvements, like better trade-offs between the message and time complexities involved. We analyze the two algorithms both mathematically and by means of simulations, always within a random-graph framework and considering relevant node-degree distributions

Local heuristics and the emergence of spanning subgraphs in complex networks

We study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks. We introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that perform well in terms of allowing every node of the network to be reached, of requiring relatively few messages and small node bandwidth for information dissemination, and also of stretching paths with respect to the underlying network only modestly. We contribute a detailed mathematical analysis of one of the heuristics and provide extensive simulation results on random graphs for both of them. These results indicate that, within certain limits, spanning subgraphs are indeed expected to emerge that perform well in respect to all requirements. We also discuss the spanning subgraphs' inherent resilience to failures and adaptability to topological changes

Two novel evolutionary formulations of the graph coloring problem

We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The second formulation, unlike the first one, does not tackle one graph at a time, but rather aims at evolving a `program' to color all graphs belonging to a class whose members all have the same number of nodes and other common attributes. The heuristics that result from these formulations have been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and have been found to be competitive when compared to the several other heuristics that have also been tested on those graphs.Comment: To appear in Journal of Combinatorial Optimizatio

Modeling the input history of programs for improved instruction-memory performance

When a program is loaded into memory for execution, the relative position of its basic blocks is crucial, since loading basic blocks that are unlikely to be executed first places them high in the instruction-memory hierarchy only to be dislodged as the execution goes on. In this paper we study the use of Bayesian networks as models of the input history of a program. The main point is the creation of a probabilistic model that persists as the program is run on different inputs and at each new input refines its own parameters in order to reflect the program's input history more accurately. As the model is thus tuned, it causes basic blocks to be reordered so that, upon arrival of the next input for execution, loading the basic blocks into memory automatically takes into account the input history of the program. We report on extensive experiments, whose results demonstrate the efficacy of the overall approach in progressively lowering the execution times of a program on identical inputs placed randomly in a sequence of varied inputs. We provide results on selected SPEC CINT2000 programs and also evaluate our approach as compared to the gcc level-3 optimization and to Pettis-Hansen reordering

Mass Generation from Lie Algebra Extensions

Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg-Salam theory are present, and a few others which are nevertheless consistent within the model.Comment: 11 pages; revtex; title and PACS have been changed; comments included in the manuscrip

Analyses of shocked quartz at the global K-P boundary indicate an origin from a single, high-angle, oblique impact at Chicxulub

Accepted versio

Acyclic orientations with path constraints

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities