On a packet scheduling problem for smart antennas and polyhedra defined by circular-ones matrices

In [E. Amaldi, A. Capone, F. Malucelli, Circular Arc Models and Algorithms for Packet Scheduling in Smart Antennas, IV ALIO/EURO Workshop on Applied Combinatorial Optimization, see: http://www-di.inf.puc-rio.br/~celso/artigos/pucon.ps, E. Amaldi, A. Capone, F. Malucelli, Discrete models and algorithms for packet scheduling in smart antennas, 2nd Cologne Twente Workshop on Graphs and Combinatorial Optimization] E. Amaldi et al. posed a combinatorial optimization problem that arises when scheduling packets in a smart antenna. The objective is to partition the set of users so as to minimize the number of time slots needed to transmit all the given packets. Here we will present a polynomial time algorithm for solving this packet scheduling problem. More generally, the algorithm solves an integer decomposition problem for polyhedra determined by a circular-ones constraint matrix, which might make it interesting also for other cyclic scheduling problems.