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Which NP-Hard Optimization Problems Admit Non-trivial Efficient Approximation Algorithms?

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Automata, Languages and Programming (ICALP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

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Abstract

In 1991 Feige, Goldwasser, Lovász, Safra and Szegedy found a connection between the approximability of Max-Clique and the area of multiprover interactive proofs. What first seemed like an isolated result have developed into an entire area of research.

The connection between interactive proofs and in particular the variant called probabilistically checkable proofs or PCPs and inapproximability results for many NP-hard optimization problems has proved to be fundamental. For some optimization problems, like clique and many constraint satisfaction problems, the parameter giving the degree of inapproximability corresponds to a natural parameter in the PCP. Other times, like for colorability and the traveling salesman problem the correspondence is not as direct, but the best results are still derived from PCPs.

The basic qualitative result on the existence of efficient PCPs was given in the famous paper by Arora, Lund, Motwani, Sudan and Szegedy in 1992 but since then the quantitative results have improved considerably. For many problems we now have almost tight results while for some others our knowledge is less complete.

The goal of this talk is to give an understanding of what has happened, outline a few of the results and give at least a taste of some ingredients of the proofs involved.

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Håstad, J. (2000). Which NP-Hard Optimization Problems Admit Non-trivial Efficient Approximation Algorithms?. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_20

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  • DOI: https://doi.org/10.1007/3-540-45022-X_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

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