
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
D. FernandezBaca, A. Medepalli, "Parametric Module Allocation on Partial kTrees," IEEE Transactions on Computers, vol. 42, no. 6, pp. 738742, June, 1993.  
BibTex  x  
@article{ 10.1109/12.277293, author = {D. FernandezBaca and A. Medepalli}, title = {Parametric Module Allocation on Partial kTrees}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {6}, issn = {00189340}, year = {1993}, pages = {738742}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.277293}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Parametric Module Allocation on Partial kTrees IS  6 SN  00189340 SP738 EP742 EPD  738742 A1  D. FernandezBaca, A1  A. Medepalli, PY  1993 KW  module allocation; partial ktrees; communication graph; polynomial time; computational complexity; distributed processing; dynamic programming; graph theory; resource allocation. VL  42 JA  IEEE Transactions on Computers ER   
The problem of allocating modules to processors in a distributed system to minimize total costs when the underlying communication graph is a partial ktree and all costs are linear functions of a real parameter t is considered. It is shown that if the number of processors is fixed, the sequence of optimum assignments that are obtained as t varies from zero to infinity can be constructed in polynomial time. As an auxiliary result, a linear time separator algorithm for ktrees is developed. The implications of the results for parametric versions of the weighted vertex cover, independent set, and 01 quadratic programming problems on partial ktrees are discussed.
[1] S. Arnborg and A. Proskurowski, "Linear time algorithms for NPhard problems restricted to partialktrees,"Discr. Appl. Math., vol. 23, pp. 1124, 1989.
[2] F. Barahona, "A solvable case for quadratic 01 programming,"Discr. Appl. Math., vol. 13, pp. 2326, 1986.
[3] S. H. Bokhari, "A shortest tree algorithm for optimal assignments across space and time in a distributed processor system,"IEEE Trans. Software Eng., vol. SE7, no. 6, pp. 583589, 1981.
[4] D. FernándezBaca, "Allocating modules to processors in a distributed system,"IEEE Trans. Software Eng., vol. 15, no. 11, pp. 14271436, 1989.
[5] D. FernándezBaca and G. Slutzki, "Solving parametric problems on trees,"J. Algorithms, vol. 10, pp. 381402, 1989.
[6] V. P. Gulati, S. K. Gupta, and A. K. Mittal, "The unconstrained quadratic bivalent programming problem,"Euro. J. Oper. Res., vol. 15, pp. 121125, 1981.
[7] D. Gusfield, "Parametric combinatorial computing and a problem of module distribution,"J. ACM, no. 3, pp. 551563, 1983.
[8] O. Kariv and S. L. Hakimi, "An algorithmic approach to network location problems I: Thepcenters,"SIAM J. Appl. Math., vol. 37, pp. 513538, 1979.
[9] R. Lipton and R. Tarjan, "Applications of a planar separator theorem,"SIAM J. Comput., vol. 9, no. 3, pp. 615627, 1980.
[10] J. Matousek and R. Thomas, "Algorithms finding treedecompositions of graphs,"J. Algorithms, vol. 12, pp. 122, 1991.
[11] B. A. Reed, "Finding approximate separators and computing tree width quickly," inProc. 24th Annu. Symp. Theory Comput., 1992, pp. 221228.
[12] N. Robertson and P. D. Seymour, "Graph minors II: Algorithmic aspects of treewidth,"J. Algorithms, vol. 7, pp. 309322, 1986.
[13] J. B. Sinclair, "Optimal assignments in broadcast networks,"IEEE Trans. Comput., vol. 37, no. 5, pp. 521531, 1988.
[14] H. Stone, "Critical load factors in twoprocessor distributed systems,"IEEE Trans. Software Eng., vol. SE4, pp. 254258, 1978.
[15] D. Towsley, "Allocating programs containing branches and loops within a multiple processor system,"IEEE Trans. Software Eng., vol. SE12, pp. 10181024, Oct. 1986.
[16] J. van Leeuwen, "Graph algorithms,"Handbook of Theoretical Computer Science, J. van Leeuwen, Ed. Cambridge, MA: M.I.T. Press, 1990.