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Intractability of approximate multi-dimensional nonlinear optimization on independence systems

Jon Lee (jonlee***at***us.ibm.com)
Shmuel Onn (onn***at***ie.technion.ac.il)
Robert Weismantel (weismant***at***math.uni-magdeburg.de)

Abstract: We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate solution can be found in polynomial time. Here, using an extended Erdos-Ko-Rado theorem of Frankl, we show that for $d=2$, finding a $\rho n$-best solution requires exponential time.

Keywords: Erdos-Ko-Rado theorem, intractability, nonlinear discrete optimization

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Combinatorial Optimization (Approximation Algorithms )

Category 3: Combinatorial Optimization (Graphs and Matroids )

Citation: IBM Research Report RC24938 (January, 2010)

Download: [PDF]

Entry Submitted: 01/29/2010
Entry Accepted: 01/29/2010
Entry Last Modified: 02/01/2010

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