Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
A Subexponential Algorithm for Abstract Optimization Problems
SIAM Journal on Computing
Optimal point placement for mesh smoothing
Journal of Algorithms
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
Algorithms for k-colouring and finding maximal independent sets
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimized color gamuts for tiled displays
Proceedings of the nineteenth annual symposium on Computational geometry
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Faster Steiner Tree Computation in Polynomial-Space
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
ACM SIGACT News
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Parameterized algorithms for d-Hitting Set: The weighted case
Theoretical Computer Science
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
Exact algorithms for dominating set
Discrete Applied Mathematics
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
Journal of Computer and System Sciences
A faster algorithm for dominating set analyzed by the potential method
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Communications of the ACM
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We consider a class of multivariate recurrences frequently arising in the worst-case analysis of Davis-Putnam-style exponential-time backtracking algorithms for NP-hard problems. We describe a technique for proving asymptotic upper bounds on these recurrences, by using a suitable weight function to reduce the problem to that of solving univariate linear recurrences; show how to use quasiconvex programming to determine the weight function yielding the smallest upper bound; and prove that the resulting upper bounds are within a polynomial factor of the true asymptotics of the recurrence. We develop and implement a multiple-gradient descent algorithm for the resulting quasiconvex programs, using a real-number arithmetic package for guaranteed accuracy of the computed worst-case time bounds.