An FPTAS for minimizing the product of two non-negative linear cost functions

We consider a quadratic programming (QP) problem (Π) of the form min xT Cx subject to Ax ≥ b where C ∈ Rn×n + , rank(C) = 1 and A ∈ Rm×n , b ∈ Rm . We present an FPTAS for this problem by reformulating the QP (Π) as a parametrized LP and “rounding” the optimal solution. Furthermore, our algorithm returns an extreme point solution of the polytope. Therefore, our results apply directly to 0-1 problems for which the convex hull of feasible integer solutions is known such as spanning tree, matchings and sub-modular flows. We also extend our results to problems for which the convex hull of the dominant of the feasible integer solutions is known such as s, t-shortest paths and s, t-min-cuts. For the above discrete problems, the quadratic program Π models the problem of obtaining an integer solution that minimizes the product of two linear non-negative cost functions.

• Type: Journal
• Year: 2011
• Where: MP
• Authors: Vineet Goyal, Latife Genç Kaya, R. Ravi
• Keywords: Feasible Integer Solutions, Integer Solution, Intelligent Agents, MP 2011, Solution