Some Simplified NP-Complete Graph Problems

@article{Garey1976SomeSN,
  title={Some Simplified NP-Complete Graph Problems},
  author={M. R. Garey and David S. Johnson and Larry J. Stockmeyer},
  journal={Theor. Comput. Sci.},
  year={1976},
  volume={1},
  pages={237-267}
}

Figures and Tables from this paper

A note on "Some simplified NP-complete graph problems"

It is shown that the degree-bounds of the directed Hamiltonian circuit with node-degree bounded by 3-out, 1-in or 1- out, 3-in is NP-complete by the following construction~ Expand each node by.

Node-and edge-deletion NP-complete problems

This paper shows that if &pgr; belongs to a rather broad class of properties then the node-deletion problem is NP-complete, and the same is true for several restrictions of it.

MSOL Restricted Contractibility to Planar Graphs

An FPT algorithm is given in time O ( n 2 f ( k ) ) which solves P- RestrictedContract and can solve the l-subgraph contractibility problem in which the edges of the set S are required to form disjoint connected subgraphs of size at most l.

Planar Graphs and Partial k-Trees

It is proved that any Hamiltonian planar graph on n vertices can be decomposed into a forest and a graph of O(log n) treewidth, and provided an efficient algorithm for constructing this decomposition.

Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth

It is shown that for 2-coloring, for bipartite perfect matching, and for several variants of disjoint paths, the straightforward NC 1 upper bound may be improved to AC 0[2], ACC 0, and AC 0 respectively for bounded planar cutwidth graphs.

NP-Completeness of Max-Cut for Segment Intersection Graphs

We consider the problem of finding a maximum cut in a graph G = (V,E), that is, a partition V1∪̇V2 of V such that the number of edges between V1 and V2 is maximum. It is well known that the decision

The Complexity of some Problems Related to Graph 3-colorability

On the hardness of approximating N P witnesses

It is shown that for many of the well known NP-complete problems it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution.

Fair Edge Deletion Problems on Tree-Decomposable Graphs and Improper Colorings ?

Every problem expressible in MSOL is solvable in polynomial time with the fair objective function, on graphs with bounded tree-width, and a Θ( √ n)-approximation algorithm is described.

On the Complexity of Approximating Colored-Graph Problems

This paper proves explicit lower bounds on the approximability of some graph problems restricted to instances which are already colored with a constant number of colors and proposes a generalization of the analysis of the complexity of approximating colored-graph problems to the complexityof approximating approximated optimization problems.
...

References

SHOWING 1-10 OF 17 REFERENCES

Approximation algorithms for combinatorial problems

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 0(nε), where n is the problem size and ε> 0 depends on the algorithm.

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

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.

Permutation Graphs and Transitive Graphs

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.

Optimal linear-ordering.

If G is a rooted tree, an algorithm is presented which requires $O( {n\log n} )$ operations, which establishes a lower bound on the total wire length.

The complexity of theorem-proving procedures

  • S. Cook
  • Mathematics, Computer Science
    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

Reducibility Among Combinatorial Problems

  • R. Karp
  • Computer Science
    50 Years of Integer Programming
  • 1972
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.

Fast Algorithms for Bin Packing

Polynomial complete scheduling problems

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.

Algorithms for a maximum clique and a maximum independent set of a circle graph

Efficient algorithms for finding a maximum clique and a maximum independent set of circle graphs that require at most n3 steps, where n is the number of vertices in the graph.