Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

2011 ◽  
Vol 53 (6) ◽  
pp. 280-286 ◽  
Author(s):  
Bodo Manthey ◽  
Heiko Röglin
Keyword(s):  
Analysis Of Algorithms ◽  
Worst Case ◽  
Smoothed Analysis

scholarly journals A further analysis of Cuckoo Hashing with a Stash and Random Graphs of Excess r

2010 ◽  
Vol Vol. 12 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Reinhard Kutzelnigg
Keyword(s):  
Analysis Of Algorithms ◽  
Hash Table ◽  
Saddle Point Method ◽  
Access Time ◽  
Worst Case ◽  
Cuckoo Hashing ◽  
Original Algorithm ◽  
International Audience ◽  
Significant Probability ◽  
Table Data

Analysis of Algorithms International audience Cuckoo hashing is a hash table data structure offering constant access time, even in the worst case. As a drawback, the construction fails with small, but practically significant probability. However, Kirsch et al. (2008) showed that a constant-sized additional memory, the so called stash, is sufficient to reduce the failure rate drastically. But so far, using a modified insertion procedure that demands additional running time to look for an admissible key is required. As a major contribution of this paper, we show that the same bounds on the failure probability hold even without this search process and thus, the performance increases. Second, we extend the analysis to simplified cuckoo hashing, a variant of the original algorithm offering increased performance. Further, we derive some explicit asymptotic approximations concerning the number of usual resp. bipartite graphs related to the data structures. Using these results, we obtain much more precise asymptotic expansions of the success rate. These calculations are based on a generating function approach and applying the saddle point method. Finally, we provide numerical results to support the theoretical analysis.

Worst-Case and Probabilistic Analysis of Algorithms for a Location Problem

1980 ◽  
Vol 28 (4) ◽  
pp. 847-858 ◽  
Author(s):  
Gerard Cornuejols ◽  
George L. Nemhauser ◽  
Laurence A. Wolsey
Keyword(s):  
Probabilistic Analysis ◽  
Location Problem ◽  
Analysis Of Algorithms ◽  
Worst Case ◽  
Probabilistic Analysis Of Algorithms
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