Given an undirected weighted graph G = (V,E) with vertex set V, edge set E and weights wi ∈ R associated to V or to E. Minimum weighted k-Cardinality tree problem (k-CARD for short) consists of finding a subtree of G with exactly k edges whose sum of weights is minimum [4]. There are two versions of this problem: vertex-weighted and edge-weighted, if weights to V or to E are associated, respect...

A systematic analysis of the effects of spatial extension on the equilibrium frequency of cooperators and defectors in 2× 2 games is presented and compared to well mixed populations where spatial extension can be neglected. We demonstrate that often spatial extension is indeed capable of promoting cooperative behavior. This holds in particular for the prisoner’s dilemma for a small but importan...

The category of von Neumann correspondences from B to C (or von Neumann B–C–modules) is dual to the category of von Neumann correspondences from C to B via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel’s Eilenberg-Watts theorem (on functors between the categories of represen...

The High School Timetabling Problem consists in assigning timeslots and resources to events, satisfying constraints which heavily depend on the specific institution. This work deals with the problem of the ongoing III International Timetabling Competition (ITC), which includes a diverse set of instances from many educational institutions around the world. We proposed an approach based on Simula...

We study the neighborhood polynomial and complexity of its computation for chordal graphs. The a graph is generating function subsets vertices that have common neighbor. introduce parameter graphs called anchor width an algorithm to compute which runs in time if polynomially bounded. maximal number different sub-cliques clique appear as neighborhood. Furthermore we some subclasses such comparab...

The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting ...

Descent methods for combinatorial optimization proceed by performing a sequence of local changes on an initial solution which improve each time the value of an objective function until a local optimum is found. Several metaheuristics have been proposed which extend in various ways this scheme and avoid being trapped in local optima. For example, Hansen and Mladenovic have recently proposed the ...

Approximation theorems were formulated for function continuous in the neighborhood of some point x, -∞< x < ∞. Namely, upper bounds obtained approximations by their Gauss-Weierstrass singular operators terms a majorant first- and second-order continuity moduli relevant functions.

Let D(p, q) be a digraph. A function f: V → {1, 2, ..., n} is said to neighborhood prime labeling of D if it both in and out degree labeling. In this paper, we introduce the concept digraphs also investigate existence some digraphs.