An edge-coloring of a graph G1⁄4 ðV ; EÞ is a function c that assigns an integer c(e) (called color) in f 0;1;2;...g to every edge eAE so that adjacent edges are assigned different colors. An edge-coloring is compact if the colors of the edges incident to every vertex form a set of consecutive integers. The deficiency problem is to determine the minimum number of pendant edges that must be adde...

The categorical notion of monad was first introduced into computer science as a way of structuring mathematical models of programming languages. The idea has subsequently been transferred back into computing practice, influencing the design of widely-used languages and frameworks. Expressions in conventional imperative programming languages bear a superficial similarity to conventional mathemat...

A short introduction to Integer Programming (IP). Problems leading to IP models. Some modelling tricks and reformulations. Geometry of linear IP. TUM matrices. Brief notes on polyhedral analysis. Separation theory. Chvatal cut hierarchy, Gomory cuts, Disjunctive cuts, RLT cut hierarchy. Iterative methods: Branch-and-Bound, Cutting Plane, Branch-and-Cut, Branch-and-Price. Lower bounds: Lagrangia...

Suppose G is an nvertex and medge simple graph with edge set E(G). An integervalued function f: E(G) → Z is called a flow. Tutte was introduced the flow polynomial F(G, λ) as a polynomial in an indeterminate λ with integer coefficients by F(G,λ) In this paper the Flow polynomial of some dendrimers are computed.

Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: P = { (w, x) ∈ R× {0, 1}N : w ≤ f (a′x + d), b′x ≤ B } where N is a positive integer, f : R 7→ R is a concave function, a, b ∈ RN are nonnegative vectors, d is a real number and B is a positive real number. We propose a family of inequalities for the convex hull...

data envelopment analysis (dea) has been widely studied in the literature since its inception with charnes, cooper and rhodes work in 1978. the methodology behind the classical dea method is to determine how much improvements in the outputs (inputs) dimensions is necessary in order to render them efficient. one of the underlying assumptions of this methodology is that the units consume and prod...

in this paper a new method is proposed for path planning of planar manipulators amid obstacles through mathematical programming in a way that the robot’s links avoid collision with obstacles throughout their motion from an initial to a goal configuration. after inputting the workspace geometry, the shortest feasible path for the robot’s end-effector is planned toward its goal position using gen...

A function f : V (G) → {0, 1, 2} is a Roman dominating function if for every vertex with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. We introduce two fractional Roman domination parameters, γR ◦ f and γRf , from relaxations of two equivalent integer programming formulations of Roman domination (the former using open neighborhoods and the later using closed neighborhoods in the Roman...

A Mond–Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse duality theorems are established. Self duality theorem is proved. A close relationship between these variational problems and static symmetric dual minimax mixed integer mul...