Two simple methods for collision resolution in open addressing hashing are First-Come-First-Serve... more Two simple methods for collision resolution in open addressing hashing are First-Come-First-Served (FCFS) and Last-Come-First-Served (LCFS). We introduce and analyze two hybrid methods, that generalize these basic strategies. The first one uses a probabilistic approach, and the second one uses a two-phase strategy, that can be tuned to achieve better performance than FCFS and LCFS.
It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and suffi... more It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and sufficient to solve the problem of finding the values of ranks immediately above and below a specified element x in a set X of size n>1. When x turns out to be the median of X, 1.5n+n/8+O(lg n) comparisons are proven to be sufficient. n+min(k,
We analyze the performance of search trees built under a variety of insertion heuristics. The mai... more We analyze the performance of search trees built under a variety of insertion heuristics. The main results are a method to obtain asymptotic expressions for the moments of the distribution of the search time, and a proof that this distribution is asymptotically normal.
We introduce a new compacting garbage-collection algorithm with a very good averagecase performan... more We introduce a new compacting garbage-collection algorithm with a very good averagecase performance. The algorithm combines the advantages of the two most frequently used algorithms for this purpose, mark-sweep and copying algorithms. The algorithm has an average time complexity that is only linear in the number of accessible edges, and it uses only a small amount of extra storage. As
Electronic Notes in Discrete Mathematics, Apr 1, 2001
AbstractDeletions in open addressing hash tables are often handled by marking the cells as “delet... more AbstractDeletions in open addressing hash tables are often handled by marking the cells as “deleted” instead of “empty”, because otherwise the search algorithm might fail to find some of the keys. The space used by deleted cells may be reused by subsequent insertions.Intuitively, search times should deteriorate as tables become contaminated with deleted cells and, as Knuth points out, in the long run the average successful search time should approach the average unsuccessful search time.We analize the effect of a long sequence of deletions and insertions over tables that use one of three insertion disciplines: standard “first-come-first-served” (FCFS)[2], “last-come-first-served” (LCFS)[3] and “Robin Hood” (RH)[1]. We show that deletions have the predicted effect over the average search cost, but their effect over the variance differs according to the insertion discipline used. When no deletions are allowed, FCFS has a very dispersed distribution, while those of LCFS and RH are very concentrated. But we show that, after many deletions and insertions, both FCFS and LCFS approach a common steady state with high dispersion, while the distribution of RH remains concentrated. We also study the transient behaviors of these methods, doing both an asymptotic and an exact analysis.
Two simple methods for collision resolution in open addressing hashing are First-Come-First-Serve... more Two simple methods for collision resolution in open addressing hashing are First-Come-First-Served (FCFS) and Last-Come-First-Served (LCFS). We introduce and analyze two hybrid methods, that generalize these basic strategies. The first one uses a probabilistic approach, and the second one uses a two-phase strategy, that can be tuned to achieve better performance than FCFS and LCFS.
It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and suffi... more It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and sufficient to solve the problem of finding the values of ranks immediately above and below a specified element x in a set X of size n>1. When x turns out to be the median of X, 1.5n+n/8+O(lg n) comparisons are proven to be sufficient. n+min(k,
We analyze the performance of search trees built under a variety of insertion heuristics. The mai... more We analyze the performance of search trees built under a variety of insertion heuristics. The main results are a method to obtain asymptotic expressions for the moments of the distribution of the search time, and a proof that this distribution is asymptotically normal.
We introduce a new compacting garbage-collection algorithm with a very good averagecase performan... more We introduce a new compacting garbage-collection algorithm with a very good averagecase performance. The algorithm combines the advantages of the two most frequently used algorithms for this purpose, mark-sweep and copying algorithms. The algorithm has an average time complexity that is only linear in the number of accessible edges, and it uses only a small amount of extra storage. As
Electronic Notes in Discrete Mathematics, Apr 1, 2001
AbstractDeletions in open addressing hash tables are often handled by marking the cells as “delet... more AbstractDeletions in open addressing hash tables are often handled by marking the cells as “deleted” instead of “empty”, because otherwise the search algorithm might fail to find some of the keys. The space used by deleted cells may be reused by subsequent insertions.Intuitively, search times should deteriorate as tables become contaminated with deleted cells and, as Knuth points out, in the long run the average successful search time should approach the average unsuccessful search time.We analize the effect of a long sequence of deletions and insertions over tables that use one of three insertion disciplines: standard “first-come-first-served” (FCFS)[2], “last-come-first-served” (LCFS)[3] and “Robin Hood” (RH)[1]. We show that deletions have the predicted effect over the average search cost, but their effect over the variance differs according to the insertion discipline used. When no deletions are allowed, FCFS has a very dispersed distribution, while those of LCFS and RH are very concentrated. But we show that, after many deletions and insertions, both FCFS and LCFS approach a common steady state with high dispersion, while the distribution of RH remains concentrated. We also study the transient behaviors of these methods, doing both an asymptotic and an exact analysis.
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