
Hard and Easy Instances of LTromino Tilings
In this work we study tilings of regions in the square lattice with Lsh...
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Necessary and Sufficient Condition for Satisfiability of a Boolean Formula in CNF and its Implications on P versus NP problem
In this paper, a necessary and sufficient condition for satisfiability o...
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A polynomial time parallel algorithm for graph isomorphism using a quasipolynomial number of processors
The Graph Isomorphism (GI) problem is a theoretically interesting proble...
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On the tractability of the maximum independent set problem
The maximum independent set problem is a classical NPcomplete problem i...
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On Restricted Disjunctive Temporal Problems: Faster Algorithms and Tractability Frontier
In 2005 Kumar studied the Restricted Disjunctive Temporal Problem (RDTP)...
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P≠ NP
The whole discussion is divided into two parts: one is for Σ≥ 2 (gener...
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The Computational Complexity of Understanding Network Decisions
For a Boolean function Φ{0,1}^d→{0,1} and an assignment to its variables...
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On Salum's Algorithm for X3SAT
This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of Oneinthree 3SAT: P = NP." Salum purports to give a polynomialtime algorithm that solves the NPcomplete problem X3SAT, thereby claiming P = NP. The algorithm, in short, fixes the polarity of a variable, carries out simplifications over the resulting formula to decide whether to keep the value assigned or flip the polarity, and repeats with the remaining variables. One thing this algorithm does not do is backtrack. We give an illustrative counterexample showing why the lack of backtracking makes this algorithm flawed.
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