# Some simplified NP-complete problems

@inproceedings{Garey1974SomeSN, title={Some simplified NP-complete problems}, author={M. R. Garey and David S. Johnson and Larry J. Stockmeyer}, booktitle={STOC '74}, year={1974} }

It is widely believed that showing a problem to be NP-complete is tantamount to proving its computational intractability. In this paper we show that a number of NP-complete problems remain NP-complete even when their domains are substantially restricted. First we show the completeness of SIMPLE MAX CUT (MAX CUT with edge weights restricted to value 1), and, as a corollary, the completeness of the OPTIMAL LINEAR ARRANGEMENT problem. We then show that even if the domains of the NODE COVER and…

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## References

SHOWING 1-10 OF 22 REFERENCES

Approximation Algorithms for Combinatorial Problems

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1974

For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.

The complexity of theorem-proving procedures

- Computer Science, MathematicsSTOC
- 1971

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…

Planar 3-colorability is polynomial complete

- Computer ScienceSIGA
- 1973

The general problem of recognizing the set of pairs (G,k), where k is a positive integer and G is a graph which is k-colorable, is polynomial complete as defined by Karp [I]. It is shown here that…

Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph

- Mathematics, Computer ScienceSIAM J. Comput.
- 1972

This paper presents ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set given a chordal graph.

Optimal linear-ordering.

- Mathematics
- 1973

Consider a set of n pins and $n( n - 1 )/2$ specified numbers of wire connections between all pairs of the n pins There are also n holes all in a line with adjacent holes at unit distances apart. The…

Polynomial complete scheduling problems

- Computer ScienceSOSP '73
- 1973

It is shown that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases, tantamount to showing that the scheduling problems mentioned are intractable.

Permutation Graphs and Transitive Graphs

- Computer ScienceJACM
- 1972

Algorithms for finding a maximum size clique and a minimum coloration of transitive grapl are presented and are applicable in solving problems in memo] allocation and circuit layout.

An efficient heuristic procedure for partitioning graphs

- Mathematics, Computer ScienceBell Syst. Tech. J.
- 1970

A heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems is presented.

Worst-case analysis of memory allocation algorithms

- Computer Science, MathematicsSTOC
- 1972

Four simple heuristic methods for assigning numbers of bins to a list of real numbers are considered and the worst-case performance of each is analyzed, closely bounding the maximum of the ratio of the number of bins used by each method applied to list A to the optimal quantity A*.

Complete register allocation problems

- Computer ScienceSTOC
- 1973

It is shown that several variants of the register allocation problem for straight line programs are polynomial complete, and the case when each value is computed exactly once, and when values may be recomputed as necessary.