We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane, called terminals, find a Steiner tree with at most k Steiner points such that the length of the longest edge in the tree is minimized. This problem is known to be NP-hard even to approximate within ratio √ 2. We focus on finding exact solutions to the problem for a small constant k. Based o...

Chain event graphs are a model family particularly suited for asymmetric causal discrete domains. This paper describes a dynamic programming algorithm for exact learning of chain event graphs from multivariate data. While the exact algorithm is slow, it allows reasonably fast approximations and provides clues for implementing more scalable heuristic algorithms.

We report a new optimal resolution for the statistical stratification problem under proportional sampling allocation among strata. Consider a finite population of N units, a random sample of n units selected from this population and a number L of strata. Thus, we have to define which units belong to each stratum so as to minimize the variance of a total estimator for one desired variable of int...

The generalized list T -coloring is a common generalization of many graph coloring models, including classical coloring, L(p, q)-labeling, channel assignment and T -coloring. Every vertex from the input graph has a list of permitted labels. Moreover, every edge has a set of forbidden differences. We ask for such a labeling of vertices of the input graph with natural numbers, in which every vert...

It is shown that the MAX2SAT problem is NP-complete even if every variable appears in at most three clauses. However, if every variable appears in at most two clauses, it is shown that it (and even the general MAXSAT problem) can be solved in linear time. When every variable appears in at most three clauses, we give an exact algorithm for MAXSAT that takes at most O(3 n=2 n) steps where n is th...

We consider the problem of assigning transmission powers to the nodes of a wireless network in such a way that all the nodes of the network are connected by bidirectional links and the total power consumption is minimized. A new exact algorithm, based on a new integer programming model, is described in this paper together with a new preprocessing technique.

We have developed an exact model and algorithm for the delay-constrained minimum cost loop problem (DC-MCLP) of finding broadcast loops from a source node. While the traditional minimum cost loop problem (MCLP) deals with only the traffic capacity constraint served by a port of source node, the DC-MCLP deals with the mean network delay and traffic capacity constraints simultaneously. The DC-MCL...

In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem. We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.

In this study, we discuss the capacitated facility location-allocation problem with uncertain parameters in which the uncertainty is characterized by given finite numbers of scenarios. In this model, the objective function minimizes the total expected costs of transportation and opening facilities subject to the robustness constraint. To tackle the problem efficiently and effectively, an effici...

We study the tournament fixing problem (TFP), which asks whether a tournament organizer can rig a single-elimination (SE) tournament such that their favorite player wins, simply by adjusting the initial seeding. Prior results give two perspectives of TFP: on the one hand, deciding whether an arbitrary player can win any SE tournament is known to be NP-complete; on the other hand, there are a nu...