  In this paper, we tackle the problem of multi-cell resource scheduling, where
the objective is to maximize the weighted sum-rate through inter-cell
interference coordination (ICIC). The blanking method is used to mitigate the
inter-cell interference, where a resource is either used with a predetermined
transmit power or not used at all, i.e., blanked. This problem is known to be
strongly NP-hard, which means that it is not only hard to solve in polynomial
time, but it is also hard to find an approximation algorithm with guaranteed
optimality gap. In this work, we identify special scenarios where a
polynomial-time algorithm can be constructed to solve this problem with
theoretical guarantees. In particular, we define a dominant interference
environment, in which for each user the received power from each interferer is
significantly greater than the aggregate received power from all other weaker
interferers.
  We show that the strongly NP-hard problem can be tightly relaxed to a linear
programming problem in a dominant interference environment. Consequently, we
propose a polynomial-time distributed algorithm that is based on the
primal-decomposition, the projected-subgradient, and the network flow
optimization methods. In comparison with baseline schemes, simulation results
show that the proposed scheme achieves higher gains in aggregate throughput,
cell-edge throughput, and outage probability.
