Quadratic programming and combinatorial minimum weight product problems

Authors:
Walter Kern;Gerhard Woeginger
Affiliations:
Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, Enschede;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven
Venue:
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Year:
2006

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Abstract

We present a fully polynomial time approximation scheme (FPTAS) for minimizing an objective (aTx+γ)(bTx+δ) under linear constraints Ax ≤d. Examples of such problems are combinatorial minimum weight product problems such as, e.g., the following: Given a graph G=(V,E) and two edge weights ${\bf a, b}: E \to {\mathbb R}_{+}$ find an s–t path P that minimizes a(P)b(P), the product of its edge weights relative to a and b. AMS-Class: 90C20, 90C26, 90C27.