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… 
Research of NP-Complete Problems in the Class of Prefractal Graphs
NP-complete problems in graphs, such as enumeration and the selection of subgraphs with given characteristics, become especially relevant for large graphs and networks. Herein, particular statements
Planar Formulae and Their Uses
TLDR
Using these results, it is able to provide simple and nearly uniform proofs of NP-completeness for planar node cover, planar Hamiltonian circuit and line, geometric connected dominating set, and of polynomial space completeness forPlanar generalized geography.
Bandwidth constrained NP-Complete problems
TLDR
Several NP-Complete problems become easier with diminishing bandwidth, however, they remain intractable unless the bandwidth is restricted to c-log2n, for some c>0.
Ultimate greedy approximation of independent sets in subcubic graphs
TLDR
The main contribution is a new mathematical theory for the design of such greedy algorithms with efficiently computable advice and for the analysis of their approximation ratios, which achieves the ultimate approximation ratio of 5/4 for greedy on graphs with maximum degree 3.
Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs
TLDR
This work develops a full suite of new reductions for the maximum weight independent set problem and provides extensive experiments to show their effectiveness in practice on real-world graphs of up to millions of vertices and edges and shows that combining kernelization with local search produces higher-quality solutions than local search alone.
NP-Complete operations research problems and approximation algorithms
  • P. Brucker
  • Mathematics, Computer Science
    Z. Oper. Research
  • 1979
TLDR
A survey onNP-complete andNP-hard problems and on approximation algorithms is given and concepts introduced are illustrated by examples which are closely related to the knapsack problem and can be understood easily.
On isomorphisms and density of NP and other complete sets
TLDR
It is shown that complete sets in EXPTIME and EXPTAPE cannot be sparse and therefore they cannot be over a single letter alphabet, and the hardest context-sensitive languages cannot been sparse.
On the hardness of range assignment problems
  • B. Fuchs
  • Computer Science, Mathematics
    Networks
  • 2005
TLDR
Using the authors' constructions, this work can for the first time prove NP-hardness of these problems for all real distance-power gradients α > 0 (resp. α > 1 for broadcast) in 2D, and prove APX- hardness of all three problems in 3D for allα > 1.
The clique problem with multiple-choice constraints under a cycle-free dependency graph
TLDR
In an application from underground and railway timetabling, it is shown that, in comparison to a naive formulation, these results lead to significant reductions in computation time.
On the Hardness of Range Assignment Problems
  • B. Fuchs
  • Mathematics, Computer Science
    CIAC
  • 2006
TLDR
Using their constructions, this work can for the first time prove NP-hardness of these problems for all real distance-power gradients α > 0 (resp. α > 1 for Broadcast) in 2-d, and prove APX- hardness of all three problems in 3-d for allα > 1.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 22 REFERENCES
Approximation Algorithms for Combinatorial Problems
TLDR
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
  • S. Cook
  • Computer Science, Mathematics
    STOC
  • 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
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
  • F. Gavril
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1972
TLDR
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.
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
...
1
2
3
...