The bounded diameter minimum spanning tree (BDMST) problem is NP-hard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flow-based mixed integer linear programming and Miller-Tucker-Zemlin-based formulations. This article presents a new, compact 0–1 integer linear programming model, which is further strengthened by dynamically adding violated connection and cycle elimination constraints within a branch-and-cut environment. The proposed approach is empirically compared to two recently published formulations. It turns out to work well in particular on dense instances with tight diameter bounds.

In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameter-constrained minimum spanning tree (DCMST) of a given undirected, edge-weighted graph, G, is the smallest-weight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NP-complete for all values of k; 4 k (n -- 2), except when all edge-weights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree data-structure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomial-time algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter-4 tree is also used for evaluating the quality of o...

. In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices placed at them as well as deciding an assignment of users to device locations. The objective when adding the new function is to choose these locations and assignments such that the combined cost of placing the devices and routing users to their assigned device locations is minimized. This problem, which we call the device placement problem, is closely related to the simple plant location problem and the p-median problem. Like these problems, the device placement problem is NP-hard, and thus it is highly unlikely that efficient methods for solving this problem to optimality exist. We discuss and test several heuristic methods for the device placement problem, as well as a very efficient meth...

this paper we consider a restricted version of the problem of locating "access facilities", or concentration points, to permit economical connection of users to resources. This problem has been already studied [16]. Actually, we consider only one resource that does not have a important place in the optimization problem. This assumption leads to a strong relation with the problem of finding a minimum r-rooted 2-height spanning tree, giving as result conceptually easy heuristics, that are easilly implemented as well. In the next section we describe in details the restricted concentrator location problem, and some related problems often found in the literature. In section

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