By Patrik Björklund.
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3 Set Covering Formulations In this section, we reformulate MNP and MLP using set covering formulations. The LP-relaxations of the set covering formulations can be eﬃciently solved using a column generation method. The optimal solutions of the LP-relaxations also enable optimal or near-optimal integer solutions. An instance of a set covering problem is characterized by a ﬁnite set S, and a collection of sets C. Each member in C comprises a subset of the elements in S. A feasible solution is a set cover of S, that is, a subset C ⊆ C such that every element in S belongs to at least one member of C .
The minimum interference FAPH can be stated as follows: Given a set of STRXs and a set of frequencies, a set of feasible frequencies for each STRX, the minimum and maximum lengths of the MAL for each STRX, the co-channel and the adjacent channel interference for every pair of STRXs, the frequency diversity gain and the interference diversity gain, the separation 42 requirement for each STRX, as well as the separation requirements between some pairs of STRXs. The problem is to assign a MAL to each STRX, such that no separation requirement is violated, and that the total cumulative co-channel and adjacent-channel interference is minimized.
For network N40, the two values diﬀer by one slot. Our results show that the maximum possible spatial reuse in STDMA, which LP can be measured as the ratio between |N | and zN , increases by network size. 86. We note that the greedy algorithm performs well for small networks. In particular, for networks with 30 nodes or less, the schedules found by the greedy algorithm are optimal. 4%. zN 30 |A| N10 N20 N30 N40 N50 N60 26 134 176 184 296 396 LSF (CPLEX) Slots LP Time 17 – – – – – 11 24 28 21 31 – 7h30m 10h* 10h* 10h* 10h* 10h* LSCF (Column Generation) Slots LP Iter.
Applications of resource optimization in wireless networks by Patrik Björklund.