TY - JOUR

T1 - Matrix columns allocation problems

AU - Beimel, Amos

AU - Ben-Moshe, Boaz

AU - Ben-Shimol, Yehuda

AU - Carmi, Paz

AU - Chai, Eldad

AU - Kitroser, Itzik

AU - Omri, Eran

N1 - Funding Information:
The last author’s research was partially supported by the Frankel Center for Computer Science. Part of this work was done while Amos Beimel was on sabbatical at the University of California, Davis, partially supported by the David and Lucile Packard Foundation.

PY - 2009/5/17

Y1 - 2009/5/17

N2 - Orthogonal Frequency Division Multiple Access (OFDMA) transmission technique is gaining popularity as a preferred technique in the emerging broadband wireless access standards. Motivated by the OFDMA transmission technique we define the following problem: Let M be a matrix (over R) of size a × b. Given a vector of non-negative integers over(C, →) = 〈 c1, c2, ..., cb 〉 such that ∑ cj = a, we would like to allocate a cells in M such that (i) in each row of M there is a single allocation, and (ii) for each element ci ∈ over(C, →) there is a unique column in M which contains exactly ci allocations. Our goal is to find an allocation with minimal value, that is, the sum of all the a cells of M which were allocated is minimal. The nature of the suggested new problem is investigated in this paper. Efficient algorithms are suggested for some interesting cases. For other cases of the problem, NP-hardness proofs are given followed by inapproximability results.

AB - Orthogonal Frequency Division Multiple Access (OFDMA) transmission technique is gaining popularity as a preferred technique in the emerging broadband wireless access standards. Motivated by the OFDMA transmission technique we define the following problem: Let M be a matrix (over R) of size a × b. Given a vector of non-negative integers over(C, →) = 〈 c1, c2, ..., cb 〉 such that ∑ cj = a, we would like to allocate a cells in M such that (i) in each row of M there is a single allocation, and (ii) for each element ci ∈ over(C, →) there is a unique column in M which contains exactly ci allocations. Our goal is to find an allocation with minimal value, that is, the sum of all the a cells of M which were allocated is minimal. The nature of the suggested new problem is investigated in this paper. Efficient algorithms are suggested for some interesting cases. For other cases of the problem, NP-hardness proofs are given followed by inapproximability results.

KW - Allocation problems

KW - NP-completeness

KW - inapproximability

UR - http://www.scopus.com/inward/record.url?scp=64449087080&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2009.02.015

DO - 10.1016/j.tcs.2009.02.015

M3 - Article

AN - SCOPUS:64449087080

SN - 0304-3975

VL - 410

SP - 2174

EP - 2183

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 21-23

ER -