We present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Br...

Given an undirected connected graph G = (V,E) with a set V of vertices, a set E of edges, and costs cij associated to every edge [i, j] ∈ E, with i < j, the Diameter Minimum Spanning Tree Problem (DCMST) consists in finding a minimum spanning tree T = (V,E ), with E ′ ⊆ E, where the diameter required does not exceed a given positive integer value D, where 2 ≤ D ≤ |V | − 1. The diameter of a tre...

zs denotes the concatenation of a data zz and a string s, l(s) is the length of a string s, 0 < ps < 1 is a constant given to a string s if 0 < l(s) 5 D 1, ,Bs = 0 if 2(s) = D (D > 1: some integer), Q,(x;) is the product of the predicted probabilities over the time instances such that the string defined below is s. The CTW assumes that the source is some tree source: the probability of x1+1 E A...

A digraph is said to be n-unavoidable if every tournament of order n contains it as a subgraph. Let f (n) be the smallest integer such that every oriented tree is f (n)-unavoidable. Sumner (see 7]) noted that f (n) 2n ? 2 and conjetured that equality holds. HH aggkvist and Thomason established the upper bounds f (n) 12n and f (n) (4 + o(1))n. Let g(k) be the smallest integer such that every ori...

The contact process on a homogeneous tree Td of degree d + 1 ≥ 3 is known [10, 7, 13] to have three distinct phases: an extinction phase, a weak survival phase, and a strong survival phase. The existence of two qualitatively different survival phases is the most striking feature of the process, as the contact process on the integer lattice Zd, in any dimension, exhibits only one survival phase ...

The set of binary trees with n internal vertices can be totally ordered using a number of different representations. There are Cn binary trees in any such order where Cn denotes the nth Catalan number. Given a total order on the set of binary trees with n internal vertices and an integer i, 14 i4Cn, the unranking problem is to generate the binary tree whose ordinal number is i. Given a binary t...

New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with $$d\ge 3$$ ) will be presented this work. All feature a nonsmooth objective function but continuous relaxations of their set feasible solutions are convex. From these models, four convex linear and considered. Each relaxation has same as model from which it is derived. Finally, preliminary co...

We propose a modification of Petri nets with strong anticipation on position. The extension modifies transition rule by adding new term that contains an integer function the marking in differences from classic are found; for example, set markings reachable current firing enabled can either be empty or contain more than one marking. consider construction reachability graph and coverability tree....

A graph G is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u ∈ V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(lu, lv) ≤ dmax where dT,w(lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T . In this paper, we conc...

We consider the generalized version of the classical Minimum Spanning Tree problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected. We present a Variable Neighborhood Search (VNS) approach which uses three different neighborhood types. Two of them work in complementary ways in order to maximize search effectivity. Both are large ...