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A Separator Theorem for Planar Graphs
Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more…
Hints on Test Data Selection: Help for the Practicing Programmer
In many cases tests of a program that uncover simple errors are also effective in uncovering much more complex errors. This so-called coupling effect can be used to save work during the testing…
On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract)
A sound pressure level meter adapted for use in monitoring noise levels, particularly for use by law enforcement agencies wherein the device includes means for providing a logarithmic indication of…
On approximately fair allocations of indivisible goods
In the presence of indivisibilities, it is shown that there exist allocations in which the envy is bounded by the maximum marginal utility, and an algorithm for computing such allocations is presented.
DNA solution of hard computational problems.
- R. Lipton
- Computer ScienceScience
- 28 April 1995
DNA experiments are proposed to solve the famous "SAT" problem of computer science and have the potential to yield vast speedups over conventional electronic-based computers for such search problems.
Some connections between nonuniform and uniform complexity classes
This work aims to understand when nonuniform upper bounds can be used to obtain uniform upper bounds, and how to relate it to more common notions.
Playing large games using simple strategies
The existence of ε-Nash equilibrium strategies with support logarithmic in the number of pure strategies is proved and it is proved that if the payoff matrices of a two person game have low rank then the game has an exact Nash equilibrium with small support.
Applications of a planar separator theorem
Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices. This separator theorem, in combination with a…
Generalized nested dissection
It is shown that sparse Gaussian elimination is efficient for any class of graphs which have good separator, and conversely that graphs without good separators are not amenable to sparse GaRussian elimination.
Reduction: a method of proving properties of parallel programs
- R. Lipton
- Computer ScienceCACM
- 1 December 1975
Correctness proofs of a parallel system can often be greatly simplified because the assumption that a statement is indivisible can be relaxed and still preserve properties such as halting.