An FPTAS for Minimizing the Product of Two Non-negative Linear Co.pdf.pdf' (155.84 kB)
An FPTAS for Minimizing the Product of Two Non-negative Linear Cost Functions
journal contribution
posted on 2006-09-01, 00:00 authored by Vineet Goyal, Latife Genç-Kaya, Ramamoorthi RaviRamamoorthi RaviWe consider a quadratic programming (QP) problem (∏) of the form min xTCx 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 (∏) as a parameterized 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.
They also apply 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
∏ models the problem of obtaining an integer solution that minimizes the product of two linear non-negative
cost functions.