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 Title: Ss/tdma Time Slot Assignment With Generalized Switching Modes Author(s): Lewandowski, James Louis Department / Program: Computer Science Discipline: Computer Science Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Computer Science Abstract: A number of problems which arise from the time slot assignment problem for satellite communications using the satellite-switched time division multiple access (SS/TDMA) method are studied. Given an m x n real matrix T, and a set of (0, 1)-matrices {Z(,1), Z(,2), (.)(.)(.) , Z(,(nu))}, the optimization problem we wish to solve is to find non-negative real constants (gamma)(,1), (gamma)(,2), ... , (gamma)(,(nu)) so that(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)is minimized, and where the inequality is implied for each corresponding entry. Although this problem can be posed as a linear program, more efficient algorithms are presented here for several special cases. We first consider the case where each Z(,i) has a specified number of ones in each row and column. For two vectors (rho) = {(rho)(,1), (rho)(,2), (.)(.)(.) , (rho)(,m)} and (lamda) = {(lamda)(,1), (lamda)(,2), (.)(.)(.) , (lamda)(,n)} of positive integers where(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)we define the set U((rho), (lamda)) to be the set of all (0, 1)-matrices which have exactly (rho)(,i) ones in the i('th) row for all i, and exactly (lamda)(,j) ones in the j('th) column for all j. A complete characterization of the class of real matrices which can be written as a positive sum of matrices in U((rho), (lamda)) is given. This result provides a generalization of the Birkhoff-Von Neumann Theorem. Also for a given T, an algorithm is presented which will solve, if possible, the above optimization problem for this set of (0, 1)-matrices. The optimization problem does not always have a feasible solution, and a complete characterization of the conditions needed for the existence of one is given. In the above expression, using these (0, 1)-matrices, (nu) can be as large as O(n('2)). In SS/TDMA applications, it is desirable to have a small value for (nu). As a second problem we consider a fixed set Z = {Z(,1), Z(,2), (.)(.)(.) , Z(,l)} for (0, 1)-matrices, where l is proportional to O(n). Given such a set of matrices, which satisfy certain constraints, we have an efficient algorithm which solves the above optimization problem for these matrices. Issue Date: 1983 Type: Text Description: 120 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983. URI: http://hdl.handle.net/2142/69516 Other Identifier(s): (UMI)AAI8324594 Date Available in IDEALS: 2014-12-15 Date Deposited: 1983
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