A common schema for dynamic programming and branch and bound algorithms
Journal of the ACM (JACM)
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Randomized algorithms
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Greedy strikes back: improved facility location algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximate Algorithms for the 0/1 Knapsack Problem
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Approximation algorithms
Introduction to Algorithms
Priority algorithms for makespan minimization in the subset model
Information Processing Letters
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
On the Equivalence between the Primal-Dual Schema and the Local-Ratio Technique
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Mathematical Structures Underlying Greedy Algorithms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Models of greedy algorithms for graph problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Toward a Model for Backtracking and Dynamic Programming
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Fast approximation algorithms for knapsack problems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
How well can primal-dual and local-ratio algorithms perform?
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Priority algorithms for graph optimization problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Note: On exponential time lower bound of Knapsack under backtracking
Theoretical Computer Science
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Can we optimally solve Max2SAT in (say) time (|F| log|F|) where |F| is the length of formula F. Of course, since Max2SAT is NP-complete, we can confidently rely on our strongly held belief that no NP-hard problem can be solved optimally in polynomial time. But obtaining unconditional complexity lower bounds (even linear or near linear bounds) remains the central challenge of complexity theory. In the complementary fields of complexity theory and that of algorithm design and analysis, we ask questions such as “what is the best polynomial time approximation ratio” that can be achieved for Max2SAT. The best negative results are derived from the beautiful development of PCP proofs. In terms of obtaining better approximation algorithms, we appeal to a variety of algorithmic techniques, including very basic techniques such as greedy algorithms, dynamic programming (with scaling), divide and conquer, local search and some more technically involved methods such as LP relaxation and randomized rounding, semi-definite programming (see [34] and [30] for an elegant presentation of these randomized methods and the concept of derandomization using conditional expectations). A more refined question might ask “what is the best approximation ratio (for a given problem such as Max2SAT) that can be obtained in (say) time O(n logn)” where n is the length of the input in some standard representation of the problem. What algorithmic techniques should we consider if we are constrained to time O(n logn)?