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A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas
TLDR
A simple constructive algorithm for the evaluation of formulas having two literals per clause, which runs in linear time on a random access machine.
Recognizing Disguised NR(1) Instances of the Satisfiability Problem
  • Bengt Aspvall
  • Mathematics, Computer Science
    J. Algorithms
  • 1 March 1980
TLDR
It is straightforward to show that NR(2)SAT is NP-complete, and whether a given CNF expression can be transformed into an equivalent NR(1) expression with at most a polynomial increase in the length of the expression is determined.
A Polynomial Time Algorithm for Solving Systems of Linear Inequalities with Two Variables per Inequality
TLDR
A constructive algorithm for solving systems of linear inequalities (LI) with at most two variables per inequality with time complexity O(mn^3 I) on a random access machine.
A polynomial time algorithm for solving systems of linear inequalities with two variables per inequality
  • Bengt Aspvall, Y. Shiloach
  • Mathematics, Computer Science
    20th Annual Symposium on Foundations of Computer…
  • 29 October 1979
TLDR
A constructive algorithm for solving systems of linear inequalities (LI) with at most two variables per inequality with polynomial in the size of the input is presented.
Graph Coloring Using Eigenvalue Decomposition
Determining whether the vertices of a graph can be colored using $k$ different colors so that no two adjacent vertices receive the same color is a well-known NP-complete problem. Graph coloring is
Selecting among scheduled projects
TLDR
A rule for optimally selecting m among n scheduled projects under discounting is demonstrated, which applies to situations of restricted choice in sequential developments of resource deposits.
Khachiyan's Linear Programming Algorithm
TLDR
L. G. Khachiyan's polynomial time algorithm for determining whether a system of linear inequalities is satisfiable is presented together with a proof of its validity and can be used to solve linear programs in polynometric time.
Approximations for the general block distribution of a matrix
The general block distribution of a matrix is a rectilinear partition of the matrix into orthogonal blocks such that the maximum sum of the elements within a single block is minimized. This
The dinner table problem
This report contains two papers inspired by the "dinner table problem": If n people are seated randomly around a circular table for two meals, what is the probability that no two people sit together
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