In the drug design process, one wants to construct chemical compounds with certain properties. In order to establish the mathematical basis for the connections between molecular structures and physicochemical properties of chemical compounds, some so-called structure-descriptors or ”topological indices” have been put forward. Among them, the Wiener index is one of the most important. A long sta...

We compare two branch-and-price approaches for the cutting stock problem. Each algorithm is based on a different integer programming formulation of the column generation master problem. One formulation results in a master problem with 0–1 integer variables while the other has general integer variables. Both algorithms employ column generation for solving LP relaxations at each node of a branch-...

A graph G is said to be t-tough if |S| ≥ t · ω(G − S) for any subset S of V (G) with ω(G− S) ≥ 2, where ω(G− S) is the number of components in G− S. Win proved that for any integer n ≥ 3 every 1 n−2 -tough graph has a spanning tree with maximum degree at most n. In this paper, we investigate t-tough graphs including the cases where t / ∈ {1, 1 2 , 1 3 , . . .}, and consider spanning trees in su...

In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NP-hard in general but becomes tractable when the network has low tree-width. Since the inference problem is common in many application areas, we provide a practical algorithm for learning bounded tree-width Bayesian networks. We cast this problem as an integer linear program ...

In this paper, we investigate the use of Gomory's mixed integer cuts within a branch-and-cut framework. It has been argued in the literature that \a marriage of classical cutting planes and tree search is out of the question as far as the solution of large-scale combinatorial optimization problems is concerned" 16] because the cuts generated at one node of the search tree need not be valid at o...

The clustered chromatic number of a class of graphs is the minimum integer k such that for some integer c every graph in the class is k-colourable with monochromatic components of size at most c. We prove that for every graph H , the clustered chromatic number of the class of H-minor-free graphs is tied to the tree-depth of H . In particular, if H has tree-depth t then every H-minor-free graph ...

We consider the problem of designating hazardous materials routes in and through a major population center. Initially, we restrict our attention to a minimally connected network (a tree) where we can predict accurately the flows on the network. We formulate the tree design problem as an integer programming problem with an objective of minimizing the total transport risk. Such design problems of...

In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard notion of sequential cutting planes...

Broadcasting means the distribution of packets from a certain source to all other hosts. One of the possible efficient implementations of broadcasting is to construct a spanning tree rooted at a given source such that each host can receive a copy of the broadcast packet originating from the source. Since the operations of most hosts in wireless networks mainly rely on battery power, in this pap...