By Manuel Blum (auth.), My T. Thai, Sartaj Sahni (eds.)

This publication constitutes the court cases of the sixteenth Annual foreign convention on Computing and Combinatorics, held in Nha Trang, Vietnam, in July 2010.

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Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2009) 15. : Computers and Intractability: A Guide to the Theory of NP–Completeness. Freeman, San Francisco (1979) 16. : Parameterized complexity of vertex cover variants. Theory of Computing Systems 41(3), 501–520 (2007) 17. : Asymptotic formulae in combinatory analysis. Proceedings of the London Mathematical Society 17 (1918) 18. : Reducibility among combinatorial problems. W. ) Complexity of Computer Communications, pp. 85–103 (1972) The Curse of Connectivity: t-Total Vertex (Edge) Cover 43 19.

Springer, Heidelberg (2009) 7. : Vertex Cover: Further observations and further improvements. Journal of Algorithms 41(2), 280–301 (2001) 8. : Improved parameterized upper bounds for Vertex Cover. , Urzyczyn, P. ) MFCS 2006. LNCS, vol. 4162, pp. 238–249. Springer, Heidelberg (2006) 9. : Introduction to Algorithms, 2nd edn. The MIT Press, Cambridge (2001) 10. : Graph Theory, 3rd edn. Springer, Heidelberg (2005) 11. : Incompressibility through Colors and IDs. , Thomas, W. ) ICALP 2009. LNCS, vol.

N} (the last m coordinates). 2 we obtain: n−m PX n An Yi Zi |W − PX n An |W PYi Zi |X n An ≤ (n − m) log i=1 1 . Pr[W ] Since the strategy is No-Signaling: n−m PX n An Yi Zi |W − PX n An |W PZi Yi |Xi ≤ (n − m) log i 1 . Pr[W ] This can be written as: n−m PX n An Yi Zi |W − PXi |W PX −i An |Xi ,W PZi Yi |Xi ≤ (n − m) log i 1 . 4, there exists a distribution QX −i An Y −i B n Y −i C n |Xi =x,Yi =y,Zi =z which can be implemented by a No-Signaling function and satisfy: n−m PXY Z QX −i An Y −i B n Y −i C n |XY Z − PXY ZX −i An Y −i B n Y −i C n |W ≤ 13 (n − m) log i=1 1 .

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