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A new 0–1 ILP approach for the bounded diameter minimum spanning tree problem
 Proceedings of the 2nd International Network Optimization Conference
, 2005
"... The bounded diameter minimum spanning tree (BDMST) problem is NPhard 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 flowbased mixed integer linear programming and Miller ..."
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Cited by 13 (7 self)
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The bounded diameter minimum spanning tree (BDMST) problem is NPhard 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 flowbased mixed integer linear programming and MillerTuckerZemlinbased 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 branchandcut 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.
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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Cited by 8 (0 self)
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight 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 NPcomplete for all values of k; 4 k (n  2), except when all edgeweights 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 datastructure, 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 polynomialtime 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 diameter4 tree is also used for evaluating the quality of o...
Models and branchandcut algorithms for the Steiner tree problem with revenues, budget and hop constraints
, 2006
"... ..."
On the boundedhop MST problem on random Euclidean instances
 In Mauricio G. C
, 2007
"... is almost optimal for the ..."
Lower and upper bounds for the spanning tree with minimum branch vertices
, 2009
"... Abstract. We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem ..."
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Abstract. We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and compare different relaxations of them, namely lagrangian relaxation, continuous relaxation, mixed integercontinuous relaxation. We approach the solution of the Lagrangian dual both by means of a standard subgradient method and an adhoc finite ascent algorithm based on updating one multiplier at the time. We provide numerical result comparison of all the considered relaxations on a wide set of benchmark instances. A useful followup of tackling the Lagrangian dual is the possibility of getting a feasible solution for the original problem with no extra costs. We evaluate the quality of the resulting upper bound by comparison either with the optimal solution, whenever available, or with the feasible solution provided by some existing heuristic algorithms.
Efficient Execution Plans for Distributed Skyline Query Processing
"... In this paper, we study the generation of efficient execution plans for skyline query processing in largescale distributed environments. In such a setting, each server stores autonomously a fraction of the data, thus all servers need to process the skyline query. An execution plan defines the order ..."
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Cited by 1 (0 self)
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In this paper, we study the generation of efficient execution plans for skyline query processing in largescale distributed environments. In such a setting, each server stores autonomously a fraction of the data, thus all servers need to process the skyline query. An execution plan defines the order in which the individual skyline queries are processed on different servers, and influences the performance of query processing. Querying servers consecutively reduces the amount of transferred data and the number of queried servers, since skyline points obtained by one server prune points in the subsequent servers, but also increases the latency of the system. To address this tradeoff,weintroducea novel framework, called SkyPlan, for processing distributed skyline queries that generates execution plans aiming at optimizing the performance of query processing. Thus, we quantify the gain of querying consecutively different servers. Then, execution plans are generated that maximize the overall gain, while also taking into account additional objectives, such as bounding the maximum number of hops required for the query or balancing the load on different servers fairly. Finally, we present an algorithm for distributed processing based on the generated plan that continuously refines the execution plan during innetwork processing. Our framework consistently outperforms the stateoftheart algorithm.
Placement and Range Assignment in PowerAware Radio Networks
, 2007
"... Due to the extraordinary growth in the demand of mobile communication services in general, design of efficient systems for providing specialized services has also become an important issue in wireless mobility research. Broadly speaking, there are two major models for wireless networking: singleho ..."
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Due to the extraordinary growth in the demand of mobile communication services in general, design of efficient systems for providing specialized services has also become an important issue in wireless mobility research. Broadly speaking, there are two major models for wireless networking: singlehop and multihop. The single
A Distributed Protocol for the BoundedHops Convergecast in AdHoc Networks
 In Proc. of AdHoc Now
, 2006
"... Abstract. Given a set S of points (stations) located in the ddim. Euclidean space and a root b ∈ S, the hhops Convergecast problem asks to find for a minimal energycost range assignment which allows to perform the convergecast primitive (i.e. node accumulation) towards b in at most h hops. For t ..."
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Abstract. Given a set S of points (stations) located in the ddim. Euclidean space and a root b ∈ S, the hhops Convergecast problem asks to find for a minimal energycost range assignment which allows to perform the convergecast primitive (i.e. node accumulation) towards b in at most h hops. For this problem no polynomial time algorithm is known even for h = 2. The main goal of this work is the design of an efficient distributed heuristic (i.e. protocol) and the analysis (both theoretical and experimental) of its expected solution cost. In particular, we introduce an efficient parameterized randomized protocol for hhops Convergecast and we analyze it on random instances created by placing n points uniformly at random in a dcube of side length L. We prove that for h = 2, its expected approximation ratio is bounded by some constant factor. Finally, for h = 3,..., 8, we provide a wide experimental study showing that our protocol has very good performances when compared with previously introduced (centralized) heuristics. 1
On the boundedhop MST problem on . . .
, 2006
"... The dDim hhops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimumcost spanning tree for S rooted at s with height at most h. We investigate the problem for any constant h and d> 0. We prove the first non trivial lower bound ..."
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The dDim hhops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimumcost spanning tree for S rooted at s with height at most h. We investigate the problem for any constant h and d> 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lowerbound holds with high probability). Then we introduce an easytoimplement, fast divide et impera heuristic and we prove that its solution cost matches the lower bound.
On the boundedhop MST problem on random Euclidean instances
"... The dDim hhops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimumcost spanning tree for S rooted at s with height at most h. We investigate the problem for any constant h and d> 0. We prove the first non trivial lower bound ..."
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The dDim hhops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimumcost spanning tree for S rooted at s with height at most h. We investigate the problem for any constant h and d> 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lowerbound holds with high probability). Then we introduce an easytoimplement, fast divide et impera heuristic and we prove that its solution cost matches the lower bound. 1