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HashBased Techniques for HighSpeed Packet Processing
"... Abstract Hashing is an extremely useful technique for a variety of highspeed packetprocessing applications in routers. In this chapter, we survey much of the recent work in this area, paying particular attention to the interaction between theoretical and applied research. We assume very little bac ..."
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Abstract Hashing is an extremely useful technique for a variety of highspeed packetprocessing applications in routers. In this chapter, we survey much of the recent work in this area, paying particular attention to the interaction between theoretical and applied research. We assume very little background in either the theory or applications of hashing, reviewing the fundamentals as necessary. 1
Maximum matchings in random bipartite graphs and the space utilization of cuckoo hashtables
, 2009
"... We study the the following question in Random Graphs. We are given two disjoint sets L, R with L  = n = αm and R  = m. We construct a random graph G by allowing each x ∈ L to choose d random neighbours in R. The question discussed is as to the size µ(G) of the largest matching in G. When consi ..."
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We study the the following question in Random Graphs. We are given two disjoint sets L, R with L  = n = αm and R  = m. We construct a random graph G by allowing each x ∈ L to choose d random neighbours in R. The question discussed is as to the size µ(G) of the largest matching in G. When considered in the context of Cuckoo Hashing, one key question is as to when is µ(G) = n whp? We answer this question exactly when d is at least three. We also establish a precise threshold for when Phase 1 of the KarpSipser Greedy matching algorithm suffices to compute a maximum matching whp.
HistoryIndependent Cuckoo Hashing
"... Cuckoo hashing is an efficient and practical dynamic dictionary. It provides expected amortized constant update time, worst case constant lookup time, and good memory utilization. Various experiments demonstrated that cuckoo hashing is highly suitable for modern computer architectures and distribute ..."
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Cited by 8 (4 self)
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Cuckoo hashing is an efficient and practical dynamic dictionary. It provides expected amortized constant update time, worst case constant lookup time, and good memory utilization. Various experiments demonstrated that cuckoo hashing is highly suitable for modern computer architectures and distributed settings, and offers significant improvements compared to other schemes. In this work we construct a practical historyindependent dynamic dictionary based on cuckoo hashing. In a historyindependent data structure, the memory representation at any point in time yields no information on the specific sequence of insertions and deletions that led to its current content, other than the content itself. Such a property is significant when preventing unintended leakage of information, and was also found useful in several algorithmic settings. Our construction enjoys most of the attractive properties of cuckoo hashing. In particular, no dynamic memory allocation is required, updates are performed in expected amortized constant time, and membership queries are performed in worst case constant time. Moreover, with high probability, the lookup procedure queries only two memory entries which are independent and can be queried in parallel. The approach underlying our construction is to enforce a canonical memory representation on cuckoo hashing. That is, up to the initial randomness, each set of elements has a unique memory representation.
Backyard Cuckoo Hashing: Constant WorstCase Operations with a Succinct Representation
, 2010
"... The performance of a dynamic dictionary is measured mainly by its update time, lookup time, and space consumption. In terms of update time and lookup time there are known constructions that guarantee constanttime operations in the worst case with high probability, and in terms of space consumption ..."
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Cited by 7 (3 self)
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The performance of a dynamic dictionary is measured mainly by its update time, lookup time, and space consumption. In terms of update time and lookup time there are known constructions that guarantee constanttime operations in the worst case with high probability, and in terms of space consumption there are known constructions that use essentially optimal space. In this paper we settle two fundamental open problems: • We construct the first dynamic dictionary that enjoys the best of both worlds: we present a twolevel variant of cuckoo hashing that stores n elements using (1+ϵ)n memory words, and guarantees constanttime operations in the worst case with high probability. Specifically, for any ϵ = Ω((log log n / log n) 1/2) and for any sequence of polynomially many operations, with high probability over the randomness of the initialization phase, all operations are performed in constant time which is independent of ϵ. The construction is based on augmenting cuckoo hashing with a “backyard ” that handles a large fraction of the elements, together with a deamortized perfect hashing scheme for eliminating the dependency on ϵ.
Optimal fast hashing
 In 28th IEEE International Conference on Computer Communications (INFOCOM
, 2009
"... Abstract—This paper is about designing optimal highthroughput hashing schemes that minimize the total number of memory accesses needed to build and access an hash table. Recent schemes often promote the use of multiplechoice hashing. However, such a choice also implies a significant increase in the ..."
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Cited by 5 (4 self)
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Abstract—This paper is about designing optimal highthroughput hashing schemes that minimize the total number of memory accesses needed to build and access an hash table. Recent schemes often promote the use of multiplechoice hashing. However, such a choice also implies a significant increase in the number of memory accesses to the hash table, which translates into higher power consumption and lower throughput. In this paper, we propose to only use choice when needed. Given some target hash table overflow rate, we provide a lower bound on the total number of needed memory accesses. Then, we design and analyze schemes that provably achieve this lower bound over a large range of target overflow values. Further, for the multilevel hash table scheme, we prove that the optimum occurs when its subtable sizes decrease in a geometric way, thus formally confirming a heuristic ruleofthumb. A. Background I.
Compact Dictionaries for VariableLength Keys and Data, with Applications
, 2007
"... We consider the problem of maintaining a dynamic dictionary T of keys and associated data for which both the keys and data are bit strings that can vary in length from zero up to the length w of a machine word. We present a data structure for this variablebitlength dictionary problem that supports ..."
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We consider the problem of maintaining a dynamic dictionary T of keys and associated data for which both the keys and data are bit strings that can vary in length from zero up to the length w of a machine word. We present a data structure for this variablebitlength dictionary problem that supports constant time lookup and expected amortized constant time insertion and deletion. It uses O(m + 3n − n log 2 n) bits, where n is the number of elements in T, and m is the total number of bits across all strings in T (keys and data). Our dictionary uses an array A[1... n] in which locations store variablebitlength strings. We present a data structure for this variablebitlength array problem that supports worstcase constanttime lookups and updates and uses O(m + n) bits, where m is the total number of bits across all strings stored in A. The motivation for these structures is to support applications for which it is helpful to efficiently store short varying length bit strings. We present several applications, including representations for semidynamic graphs, order queries on integers sets, cardinal trees with varying cardinality, and simplicial meshes of d dimensions. These results either generalize or simplify previous results.
Compact Data Structures with Fast Queries
, 2005
"... Many applications dealing with large data structures can benefit from keeping them in compressed form. Compression has many benefits: it can allow a representation to fit in main memory rather than swapping out to disk, and it improves cache performance since it allows more data to fit into the c ..."
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Cited by 4 (0 self)
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Many applications dealing with large data structures can benefit from keeping them in compressed form. Compression has many benefits: it can allow a representation to fit in main memory rather than swapping out to disk, and it improves cache performance since it allows more data to fit into the cache. However, a data structure is only useful if it allows the application to perform fast queries (and updates) to the data.
An Analysis of RandomWalk Cuckoo Hashing
"... In this paper, we provide a polylogarithmic bound that holds with high probability on the insertion time for cuckoo hashing under the randomwalk insertion method. Cuckoo hashing provides a useful methodology for building practical, highperformance hash tables. The essential idea of cuckoo hashing ..."
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Cited by 4 (2 self)
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In this paper, we provide a polylogarithmic bound that holds with high probability on the insertion time for cuckoo hashing under the randomwalk insertion method. Cuckoo hashing provides a useful methodology for building practical, highperformance hash tables. The essential idea of cuckoo hashing is to combine the power of schemes that allow multiple hash locations for an item with the power to dynamically change the location of an item among its possible locations. Previous work on the case where the number of choices is larger than two has required a breadthfirst search analysis, which is both inefficient in practice and currently has only a polynomial high probability upper bound on the insertion time. Here we significantly advance the state of the art by proving a polylogarithmic bound on the more efficient randomwalk method, where items repeatedly kick out random blocking items until a free location for an item is found. 1
Fast and compact hash tables for integer keys
 in Proc. 32nd Australasian Conf. Comput. Sci. (ACSC’09), 2009
"... A hash table is a fundamental data structure in computer science that can offer rapid storage and retrieval of data. A leading implementation for string keys is the cacheconscious array hash table. Although fast with strings, there is currently no information in the research literature on its perfor ..."
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Cited by 4 (1 self)
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A hash table is a fundamental data structure in computer science that can offer rapid storage and retrieval of data. A leading implementation for string keys is the cacheconscious array hash table. Although fast with strings, there is currently no information in the research literature on its performance with integer keys. More importantly, we do not know how efficient an integerbased array hash table is compared to other hash tables that are designed for integers, such as bucketized cuckoo hashing. In this paper, we explain how to efficiently implement an array hash table for integers. We then demonstrate, through careful experimental evaluations, which hash table, whether it be a bucketized cuckoo hash table, an array hash table, or alternative hash table schemes such as linear probing, offers the best performance—with respect to time and space— for maintaining a large dictionary of integers inmemory, on a current cacheoriented processor.