A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Communication preserving protocols for secure function evaluation
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Information and Computation
Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem
Theoretical Computer Science
Approximate local search in combinatorial optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
Completeness in approximation classes beyond APX
Theoretical Computer Science
Theoretical Computer Science
Polynomial time approximation schemes and parameterized complexity
Discrete Applied Mathematics
Approximability of identifying codes and locating--dominating codes
Information Processing Letters
Polynomial-TimeMaximisation Classes: Syntactic Hierarchy
Fundamenta Informaticae - Workshop on Combinatorial Algorithms
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
Covering the edges of bipartite graphs using K2,2 graphs
Theoretical Computer Science
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Covering Games: Approximation through Non-cooperation
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
On the performance of congestion games for optimum satisfiability problems
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Covering the edges of bipartite graphs using K2,2gaphs
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Uniform unweighted set cover: The power of non-oblivious local search
Theoretical Computer Science
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Further reflections on a theory for basic algorithms
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
On the complexity of global constraint satisfaction
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximability of bounded occurrence max ones
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Poly-APX- and PTAS-Completeness in standard and differential approximation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Logspace optimization problems and their approximability properties
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
Parameterizing MAX SNP problems above guaranteed values
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On the relative merits of simple local search methods for the MAX-SAT problem
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Approximating the unweighted k-set cover problem: greedy meets local search
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Survey: A survey on the structure of approximation classes
Computer Science Review
Local approximations for maximum partial subgraph problem
Operations Research Letters
Polynomial-TimeMaximisation Classes: Syntactic Hierarchy
Fundamenta Informaticae - Workshop on Combinatorial Algorithms
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Temporal network optimization subject to connectivity constraints
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
A note on anti-coordination and social interactions
Journal of Combinatorial Optimization
Hi-index | 0.01 |
We attempt to reconcile the two distinct views of approximation classes: syntactic and computational. Syntactic classes such as MAX SNP permit structural results and have natural complete problems, while computational classes such as APX allow us to work with classes of problems whose approximability is well understood. Our results provide a syntactic characterization of computational classes and give a computational framework for syntactic classes.We compare the syntactically defined class MAX SNP with the computationally defined class APX and show that every problem in APX can be "placed" (i.e., has approximation-preserving reduction to a problem) in MAX SNP. Our methods introduce a simple, yet general, technique for creating approximation-preserving reductions which shows that any "well"-approximable problem can be reduced in an approximation-preserving manner to a problem which is hard to approximate to corresponding factors. The reduction then follows easily from the recent nonapproximability results for MAX SNP-hard problems. We demonstrate the generality of this technique by applying it to other classes such as MAX SNP-RMAX(2) and MIN F$^{+}\Pi_2(1)$ which have the clique problem and the set cover problem, respectively, as complete problems.The syntactic nature of MAX SNP was used by Papadimitriou and Yannakakis [J. Comput. System Sci., 43 (1991), pp. 425--440] to provide approximation algorithms for every problem in the class. We provide an alternate approach to demonstrating this result using the syntactic nature of MAX SNP. We develop a general paradigm, nonoblivious local search, useful for developing simple yet efficient approximation algorithms. We show that such algorithms can find good approximations for all MAX SNP problems, yielding approximation ratios comparable to the best known for a variety of specific MAX SNP-hard problems. Nonoblivious local search provably outperforms standard local search in both the degree of approximation achieved and the efficiency of the resulting algorithms.