Planning wireless networks by shortest path

Transmitters and receivers are the basic elements of wireless networks and are characterized by a number of radio-electrical parameters. A general planning problem consists in establishing suitable values for these parameters so as to optimize some network performance indicator. In this paper we consider a version of the problem called the Power Assignment Problem (PAP), that is the problem of assigning transmission powers to the transmitters of a wireless network so as to maximize the satisfied demand. This problem has relevant practical applications both in radio-broadcasting and in mobile telephony. Typical solution approaches make use of mixed integer linear programs with huge coefficients in the constraint matrix yielding numerical inaccuracy and poor bounds and cannot be exploited to solve large instances of practical interest. In order to overcome these inconveniences, we developed a two-phase heuristic to solve large instances of PAP, namely a constructive heuristic followed by an improving local search. Both phases are based on successive shortest path computations on suitable directed graphs. Computational tests on a number of instances arising in the design of the Italian Digital Video Broadcasting are presented.