Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
Coloring heuristics for register allocation
PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
A still better performance guarantee for approximate graph coloring
Information Processing Letters
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
New approximation algorithms for graph coloring
Journal of the ACM (JACM)
Improved non-approximability results
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A spectral technique for coloring random 3-colorable graphs (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomized algorithms
Randomized graph products, chromatic numbers, and Lovasz j-function
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Derandomizing semidefinite programming based approximation algorithms
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Register allocation & spilling via graph coloring
SIGPLAN '82 Proceedings of the 1982 SIGPLAN symposium on Compiler construction
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Graphs and Hypergraphs
Coloring k-colorable graphs using smaller palettes
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximating coloring and maximum independent sets in 3-uniform hypergraphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Derandomized dimensionality reduction with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Generating Convex Polynomial Inequalities for Mixed 0–1 Programs
Journal of Global Optimization
Coloring k-colorable graphs using relatively small palettes
Journal of Algorithms
Semidefinite Programming Methods for the Symmetric Traveling Salesman Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Semidefinite Relaxation of the k -Partition Polytope Is Strong
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
The RPR2 Rounding Technique for Semidefinite Programs
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Finding Large Independent Sets in Polynomial Expected Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The side-chain positioning problem: a semidefinite programming formulation with new rounding schemes
PCK50 Proceedings of the Paris C. Kanellakis memorial workshop on Principles of computing & knowledge: Paris C. Kanellakis memorial workshop on the occasion of his 50th birthday
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
Journal of Computer and System Sciences - STOC 2001
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Multiple Access Protocol for Power-Controlled Wireless Access Nets
IEEE Transactions on Mobile Computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The Lovász Number of Random Graphs
Combinatorics, Probability and Computing
New approximation guarantee for chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
The RPR2 rounding technique for semidefinite programs
Journal of Algorithms
Tales of Hoffman: three extensions of Hoffman's bound on the graph chromatic number
Journal of Combinatorial Theory Series B
An improved algorithm for approximating the chromatic number of Gn,p
Information Processing Letters
Finding Large Independent Sets in Polynomial Expected Time
Combinatorics, Probability and Computing
Solving NP-hard semirandom graph problems in polynomial expected time
Journal of Algorithms
A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies
INFORMS Journal on Computing
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A semidefinite programming-based heuristic for graph coloring
Discrete Applied Mathematics
On the adaptable chromatic number of graphs
European Journal of Combinatorics
On the tractability of coloring semirandom graphs
Information Processing Letters
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Additive approximation algorithms for list-coloring minor-closed class of graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
A Vector Assignment Approach for the Graph Coloring Problem
Learning and Intelligent Optimization
Approximation algorithms for the weighted independent set problem in sparse graphs
Discrete Applied Mathematics
Combinatorial optimization in system configuration design
Automation and Remote Control
Random projections preserving the Hamming distance between words
Proceedings of the 2009 conference on New Directions in Neural Networks: 18th Italian Workshop on Neural Networks: WIRN 2008
SDP-Based Algorithms for Maximum Independent Set Problems on Hypergraphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
An SDP primal-dual algorithm for approximating the Lovász-theta function
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
Approximations of weighted independent set and hereditary subset problems
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On the complexity of approximating colored-graph problems extended abstract
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Communication lower bounds via the chromatic number
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Note: A simple algorithm for 4-coloring 3-colorable planar graphs
Theoretical Computer Science
Computer-aided design for microfluidic chips based on multilayer soft lithography
ICCD'09 Proceedings of the 2009 IEEE international conference on Computer design
Low-complexity non-uniform demand multicast network coding problems
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
The UGC Hardness Threshold of the Lp Grothendieck Problem
Mathematics of Operations Research
Paired approximation problems and incompatible inapproximabilities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the conditional hardness of coloring a 4-colorable graph with super-constant number of colors
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating Semidefinite Packing Programs
SIAM Journal on Optimization
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Linear index coding via semidefinite programming
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
List-coloring graphs without subdivisions and without immersions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Layout decomposition for triple patterning lithography
Proceedings of the International Conference on Computer-Aided Design
The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Wireless capacity with arbitrary gain matrix
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Explicit Dimension Reduction and Its Applications
SIAM Journal on Computing
Product rules in semidefinite programming
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Regular inference as vertex coloring
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Vertex cover in graphs with locally few colors
Information and Computation
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
SDP-based algorithms for maximum independent set problems on hypergraphs
Theoretical Computer Science
A novel approach for leveraging co-occurrence to improve the false positive error in signature files
Journal of Discrete Algorithms
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We consider the problem of coloring k-colorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3-colorable graph on n vertices with min{O(&Dgr;1/3 log1/2 &Dgr; log n), O(n1/4 log1/2 n)} colors where &Dgr; is the maximum degree of any vertex. Besides giving the best known approximation ratio in terms of n, this marks the first nontrivial approximation result as a function of the maximum degree &Dgr;. This result can be generalized to k-colorable graphs to obtain a coloring using min{O(&Dgr;1-2/k log1/2 &Dgr; log n), O(n1−3/(k+1) log1/2 n)} colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2-SAT problems. An intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the Lovász &thgr;-function. We show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number; by duality this also demonstrates interesting new facts about the &thgr;-function.