The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Planar 3-colorability is polynomial complete
ACM SIGACT News
Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
A generalized implicit enumeration algorithm for graph coloring
Communications of the ACM - Lecture notes in computer science Vol. 174
The complexity of optimization problems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the learnability of Boolean formulae
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Distributed Nodes Organization Algorithm for Channel Access in a Multihop Dynamic Radio Network
IEEE Transactions on Computers
Layer Assignment Problem for Three-Layer Routing
IEEE Transactions on Computers
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Computational limitations on learning from examples
Journal of the ACM (JACM)
The minimum consistent DFA problem cannot be approximated within and polynomial
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The minimum consistent DFA problem cannot be approximated within any polynomial
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
A new lower bound for the frequency assignment problem
IEEE/ACM Transactions on Networking (TON)
The approximability of NP-hard problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Graph coloring algorithms for fast evaluation of Curtis decompositions
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
P-Complete Approximation Problems
Journal of the ACM (JACM)
New Algorithms for Bin Packing
Journal of the ACM (JACM)
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
A Survey of Analysis Techniques for Discrete Algorithms
ACM Computing Surveys (CSUR)
Covering edges by cliques with regard to keyword conflicts and intersection graphs
Communications of the ACM
Graph Colouring by Maximal Evidence Edge Adding
PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
A Fast and Simple Local Search for Graph Coloring
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
A new approximate graph coloring algorithm
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
ACM '78 Proceedings of the 1978 annual conference
On the completeness of a generalized matching problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Automatic storage optimization
SIGPLAN '79 Proceedings of the 1979 SIGPLAN symposium on Compiler construction
Distributing a database for parallel processing is NP-hard
ACM SIGMOD Record
Automatic storage optimization
ACM SIGPLAN Notices - Best of PLDI 1979-1999
Scratchpad allocation for data aggregates in superperfect graphs
Proceedings of the 2007 ACM SIGPLAN/SIGBED conference on Languages, compilers, and tools for embedded systems
All-to-all disjoint multipath routing using cycle embedding
Computer Networks: The International Journal of Computer and Telecommunications Networking
Approximation algorithm for maximum edge coloring
Theoretical Computer Science
Enhancing PC Cluster-Based Parallel Branch-and-Bound Algorithms for the Graph Coloring Problem
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Non-approximability of just-in-time scheduling
Journal of Scheduling
A note on the approximation of the max clique problem
Information Processing Letters
Approximation algorithms for maximum edge coloring problem
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Scratchpad memory allocation for data aggregates via interval coloring in superperfect graphs
ACM Transactions on Embedded Computing Systems (TECS)
Does more connectivity help groups to solve social problems
Proceedings of the 12th ACM conference on Electronic commerce
Average-case non-approximability of optimisation problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Survey: Randomly colouring graphs (a combinatorial view)
Computer Science Review
Note: Quantum annealing of the graph coloring problem
Discrete Optimization
Average-case complexity of backtrack search for coloring sparse random graphs
Journal of Computer and System Sciences
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Graph coloring problems, in which one would like to color the vertices of a given graph with a small number of colors so that no two adjacent vertices receive the same color, arise in many applications, including various scheduling and partitioning problems. In this paper the complexity and performance of algorithms which construct such colorings are investigated. For a graph G, let &khgr;(G) denote the minimum possible number of colors required to color G and, for any graph coloring algorithm A, let A(G) denote the number of colors used by A when applied to G. Since the graph coloring problem is known to be “NP-complete,” it is considered unlikely that any efficient algorithm can guarantee A(G) = &khgr;(G) for all input graphs. In this paper it is proved that even coming close to khgr;(G) with a fast algorithm is hard. Specifically, it is shown that if for some constant r d there exists a polynomial-time algorithm A which guarantees A(G) ≤ r·&khgr;(G) + d, then there also exists a polynomial-time algorithm A which guarantees A(G) = &khgr;(G).