Matrix columns allocation problems

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, ..., c_b 〉 such that ∑ c_j = 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 c_i ∈ over(C, →) there is a unique column in M which contains exactly c_i 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.