Ayman Abdalla, Narsingh Deo, and Pankaj Gupta. Random-tree diameter and the diameter-constrained MST. Congressus Numerantium, 144:161-182, 2000. Home/Search Document Details and Download
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Greedy Heuristics and an Evolutionary Algorithm for the.. - Raidl, Julstrom (2003) (Correct)
....D = 4 on n = 19 vertices; the vertex v is its center, and (b) a tree of odd diameter D = 5 on the same vertices; v1 and v2 together form its center. heuristic and exhaustive search. Unfortunately, its time is O(n 2D ) so it is suitable only for small problem instances. Abdalla, Deo, and Gupta [1, 6] described two heuristics for the BDMST problem, without approximation guarantees. One iteratively refines an unconstrained minimum spanning tree. This heuristic is computationally expensive and does not always find a feasible solution (even on a complete graph) particularly when D is small. The ....
....a vertex in the tree with one not in the tree. The diameter of the spanning tree at each step can always be known; modifying Prim s algorithm to accommodate the diameter bound yields greedy heuristics for the BDMST problem on complete graphs. One such has been described by Abdalla, Deo, and Gupta [1]. They called it One Time Tree Construction (OTTC) Beginning at a specified start vertex, OTTC repeatedly extends the growing tree with the lowest weight edge between a tree vertex and a non tree vertex whose inclusion does not violate the diameter bound. The algorithm keeps track of the path ....
A. Abdalla, N. Deo, and P. Gupta. Random-tree diameter and the diameter constrained MST. Congressus Numerantium, 144:161--182, 2000.
Random-Tree Diameter and the DiameterConstrained MST - Abdalla, Deo, Gupta (2000) (2 citations) Self-citation (Abdalla Deo Gupta) (Correct)
....870,000 Order (n ) Error Percentage: Obs. Dia. 3.33 sqrt(n) Obs. Dia. 100 each order. As seen in Figure 2, for trees of order larger than 5000, the leafdeletion algorithm is clearly the fastest. The C source code for both algorithms is included in our technical report [2]. 3 Polynomially Solvable Cases There are four cases of the DCMST problem that can be exactly solved in polynomial time. When the diameter constraint k = n 1, an MST is the solution. When k = 2, the optimal solution is a smallest weight star, which can be computed in O(n 2 ) by comparing ....
....the OTTC and IR algorithms on the MasPar MP 1, a massively parallel SIMD machine of 8192 processors. The processors are arranged in a mesh where each processor is connected to its eight neighbors. The source code for all algorithms implemented, written in MPL C, is included in the technical report [2]. Complete graphs, K n , represented by their (n n) weight matrices, were used as input. An incomplete graph can be viewed as a complete graph in which the missing edges have infinite weight. Since the MST of a randomly generated graph has a small diameter, n O , it is not suited for ....
Abdalla, A., Deo, N., Gupta, P., "Random-Tree Diameter and the Diameter -Constrained MST," Technical Report CS-TR-00-02, University of Central Florida, Orlando, FL, 2000.
Local-Search and Hybrid Evolutionary Algorithms for Pareto.. - Knowles (2002) (7 citations) (Correct)
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Ayman Abdalla, Narsingh Deo, and Pankaj Gupta. Random-tree diameter and the diameter-constrained MST. Congressus Numerantium, 144:161-182, 2000.
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