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**11 - 17**of**17**### Distributional analysis of Robin Hood linear probing hashing with buckets

"... This paper presents the first distributional analysis of a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a bα-full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributi ..."

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This paper presents the first distributional analysis of a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a bα-full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size m and n elements. A key element in the analysis is the use of a new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets.

### Strongly History Independent Hashing with Deletion

, 2006

"... We present a strongly history independent (SHI) hash table that is fast, space efficient, and supports deletions. A hash table that supports deletions is SHI if it has a canonical memory representation up to randomness. That is, the string of random bits and current hash table contents (the set of ( ..."

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We present a strongly history independent (SHI) hash table that is fast, space efficient, and supports deletions. A hash table that supports deletions is SHI if it has a canonical memory representation up to randomness. That is, the string of random bits and current hash table contents (the set of (key, object) pairs in the hash table) uniquely determine its layout in memory, independently of the sequence of operations from initialization to the current state. Thus, the memory representation of a SHI hash table reveals exactly the information available through the hash table interface, and nothing more. Our construction also reveals a subtle connection between history independent hashing and the Gale-Shapley stable marriage algorithm [7], which may be of independent interest. Additionally, we give a general technique for converting data structures with canonical representations in a pure pointer machine model into RAM data structures of comparable performance and that are SHI with high probability. Thus we develop the last ingredient necessary to efficiently implement a host of SHI data structures on a RAM. This research is supported by NSF ITR grants CCR-0122581 (The Aladdin Center) and IIS-0121678.

### Vol. 00, No. 00, Month 200x, 1–15 Efficient data structures for sparse network representation

"... Modern-day computers are characterized by a striking contrast between the processing power of the CPU and the latency of main memory accesses. If the data processed is both large compared to processor caches and sparse or high-dimensional in nature, as is commonly the case in complex network researc ..."

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Modern-day computers are characterized by a striking contrast between the processing power of the CPU and the latency of main memory accesses. If the data processed is both large compared to processor caches and sparse or high-dimensional in nature, as is commonly the case in complex network research, the main memory latency can become a performace bottleneck. In this Article, we present a cache efficient data structure, a variant of a linear probing hash table, for representing edge sets of such networks. The performance benchmarks show that it is, indeed, quite superior to its commonly used counterparts in this application. In addition, its memory footprint only exceeds the absolute minimum by a small constant factor. The practical usability of our approach has been well demonstrated in the study of very large real-world networks.

### A Hardware Algorithm For High Speed Morpheme Extraction And Its Implementation

"... This paper describes a new hardware algorithm for morpheme extraction and its implementation on a specific miae (MEX-, the t step towed eving natur 1 ping - etom. It o shows the mie's peffo, 100-1,000 tim [ter th pemon computer. This mine c extrt morphem [rom 10,000 charer Jspese tt by hing 80, ..."

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This paper describes a new hardware algorithm for morpheme extraction and its implementation on a specific miae (MEX-, the t step towed eving natur 1 ping - etom. It o shows the mie's peffo, 100-1,000 tim [ter th pemon computer. This mine c extrt morphem [rom 10,000 charer Jspese tt by hing 80,000 morpheme dlctiosry in 1 coad. multiple text sre, w are comped ck- er dldtes, w one text stm The rithm is fropier. ted on the mhie time for the number of csndldt, while cov- tion sueti algorithms are implemented in combinational time.

### On Worst Case Robin-Hood Hashing

, 2002

"... We consider open addressing hashing, and implement it by using the Robin Hood strategy, that is, in case of collision, the element that has traveled the furthest can stay in the slot. We hash #n elements into a table of size n where each probe is independent and uniformly distributed over the tab ..."

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We consider open addressing hashing, and implement it by using the Robin Hood strategy, that is, in case of collision, the element that has traveled the furthest can stay in the slot. We hash #n elements into a table of size n where each probe is independent and uniformly distributed over the table, and # < 1 is a constant. Let Mn be the maximum search time for any of the elements in the table. We show that with probability tending to one, Mn [log 2 log n + #, log 2 log n + # ] for some constants #, # depending upon # only. This is an exponential improvement over the maximum search time in case of the standard FCFS (first come first served) collision strategy, and virtually matches the performance of multiple choice hash methods.

### Distributional Analysis of the Parking Problem and Robin Hood Linear Probing Hashing with Buckets

, 2009

"... This paper presents the first distributional analysis of both, a parking problem and a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a bα-full table is obtained, and moments and asymptotic results are derived. With the use of the ..."

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This paper presents the first distributional analysis of both, a parking problem and a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a bα-full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size m and n elements. A key element in the analysis is the use of a new family of numbers, called Tuba Numbers, that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets.

### Object-Oriented Languages Considered Harmful

"... Many theorists would agree that, had it not been for RAID, the renement of the Ethernet might never have occurred. After years of conrmed research into wide-area networks, we validate the evaluation of extreme programming. We demonstrate that although RAID can be made metamorphic, symbiotic, and sma ..."

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Many theorists would agree that, had it not been for RAID, the renement of the Ethernet might never have occurred. After years of conrmed research into wide-area networks, we validate the evaluation of extreme programming. We demonstrate that although RAID can be made metamorphic, symbiotic, and smart, expert systems can be made robust, random, and collaborative [18]. I.