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Quasiconvex Analysis of Backtracking Algorithms [article]

David Eppstein
2003 arXiv   pre-print
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 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  ...  I would like to thank Jesper Byskov and George Lueker for helpful discussions and comments on drafts of this paper, and Keith Briggs for help with programming using XR.  ... 
arXiv:cs/0304018v2 fatcat:7zpmbvdaqjg2xpcgadjok2fcg4

Quasiconvex Programming [article]

David Eppstein
2004 arXiv   pre-print
We survey algorithms for solving quasiconvex programs either numerically or via generalizations of the dual simplex method from linear programming, and describe varied applications of this geometric optimization  ...  technique in meshing, scientific computation, information visualization, automated algorithm analysis, and robust statistics.  ...  which of the cases in the analysis are the critical ones for the performance of the backtracking algorithm that generated the recurrence?  ... 
arXiv:cs/0412046v1 fatcat:pe3az4m4o5hclfidjevqibn2um

Applying Practice to Theory [article]

Ryan Williams
2008 arXiv   pre-print
We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe how linear program solvers may be used to help prove  ...  new lower bounds for satisfiability, and suggest a research program for developing new understanding in circuit complexity.  ...  For some algorithms we can get surprisingly good time bounds in terms of the total number of nodes: quasiconvex optimization uncovers interesting α i 's.  ... 
arXiv:0811.1305v1 fatcat:wngu2dipivcingv5kx2atojgc4