109:; that is, the proportion of the slots in the array that are used. As the load factor increases towards 100%, the number of probes that may be required to find or insert a given key rises dramatically. Once the table becomes full, probing algorithms may even fail to terminate. Even with good hash functions, load factors are normally limited to 80%. A poor hash function can exhibit poor performance even at very low load factors by generating significant clustering, especially with the simplest linear addressing method. Generally typical load factors with most open addressing methods are 50%, whilst
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346:(1) remove method above is only possible in linearly probed hash tables with single-slot stepping. In the case where many records are to be deleted in one operation, marking the slots for deletion and later rebuilding may be more efficient.
83:, while double hashing has poor cache performance but exhibits virtually no clustering; quadratic probing falls in-between in both areas. Double hashing can also require more computation than other forms of probing.
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For all records in a cluster, there must be no vacant slots between their natural hash position and their current position (else lookups will terminate before finding the record). At this point in the pseudocode,
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Another technique for removal is simply to mark the slot as deleted. However this eventually requires rebuilding the table simply to remove deleted records. The methods above provide
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is an implementation of an open addressing hash table with linear probing and single-slot stepping, a common approach that is effective if the hash function is good. Each of the
46:) until either the target record is found, or an unused array slot is found, which indicates that there is no such key in the table. Well-known probe sequences include:
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mark slot as occupied slot.key := slot.key slot.value := slot.value mark slot as unoccupied i := j
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move existing keys around in the array to make room for the new key. This gives better maximum search times than the methods based on probing.
384:
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Poblete; Viola; Munro. "The
Analysis of a Hashing Scheme by the Diagonal Poisson Transform". p. 95 of Jan van Leeuwen (Ed.)
339:(1) updating and removal of existing records, with occasional rebuilding if the high-water mark of the table size grows.
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operation to insert all the elements of the old array into the new larger array. It is common to increase the array size
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in which the interval between probes increases quadratically (hence, the indices are described by a quadratic function).
95:
454:, in Dictionary of Algorithms and Data Structures , Vreda Pieterse and Paul E. Black, eds. 17 September 2015.
441:, in Dictionary of Algorithms and Data Structures , Vreda Pieterse and Paul E. Black, eds. 17 September 2015.
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would naturally land in the hash table if there were no collisions. This test is asking if the record at
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i := find_slot(key) mark slot as occupied slot.key := key slot.value := value
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in which the interval between probes is fixed for each record but is computed by another hash function.
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is a vacant slot that might be invalidating this property for subsequent records in the cluster.
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426:"Robin Hood Hashing really has constant average search cost and variance in full tables"
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164:(slot is occupied) and (slot.key ≠ key) i := (i + 1) modulo num_slots
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is invalidly positioned with respect to the required properties of a cluster now that
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Rebuilding the table requires allocating a larger array and recursively using the
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The main trade offs between these methods are that linear probing has the best
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A critical influence on performance of an open addressing hash table is the
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to locate the array slot that either does or should contain a given key.
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Tenenbaum, Aaron M.; Langsam, Yedidyah; Augenstein, Moshe J. (1990),
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358:– a method of deleting from a hash table using open addressing.
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in which the interval between probes is fixed — often set to 1.
42:, or searching through alternative locations in the array (the
159:// search until we either find the key, or find an empty slot.
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find_slot(key) i := hash(key) modulo num_slots
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the table is almost full rebuild the table larger
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Hash collision resolved by linear probing (interval=1).
413:"Efficient C/C++ Programming: Smaller, Faster, Better"
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pair { key, value, occupied flag (initially unset) }
38:. With this method a hash collision is resolved by
276:// i > j: |.k..j i....| or |....j i..k.|
268:k := hash(slot.key) modulo num_slots
201:set(key, value) i := find_slot(key)
242:remove(key) i := find_slot(key)
235:, for example by doubling the old array size.
174:lookup(key) i := find_slot(key)
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379:, Prentice Hall, pp. 456–461, pp. 472,
253:mark slot as unoccupied j := i
260:j := (j + 1) modulo num_slots
270:// determine if k lies cyclically in (i,j]
137:functions use a common internal function
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285:(i < k) and (k ≤ j)
295:(k ≤ j) or (i < k)
86:Some open addressing methods, such as
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424:Patricio V. Poblete, Alfredo Viola.
319:is the raw hash where the record at
36:collision resolution in hash tables
16:Hash collision resolution technique
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209:slot.value := value
439:"Last-Come First-Served Hashing"
264:slot is unoccupied
113:typically can use up to 100%.
96:last-come-first-served hashing
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315:is such a subsequent record.
273:// i ≤ j: | i..k..j |
246:slot is unoccupied
151:pair slot, slot, ..., slot
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251:// key is not in the table
79:but is most sensitive to
377:Data Structures Using C
400:"Algorithms - ESA '94"
190:// key is not in table
24:
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452:"Robin Hood hashing"
207:// we found our key
205:slot is occupied
178:slot is occupied
281:i ≤ j
180:// key is in table
117:Example pseudocode
92:Robin Hood hashing
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111:separate chaining
88:Hopscotch hashing
77:cache performance
59:Quadratic probing
34:, is a method of
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107:load factor
363:References
331:is vacant.
195:not found
123:pseudocode
81:clustering
266:exit loop
139:find_slot
464:Category
350:See also
258:(note 2)
240:function
218:(note 1)
199:function
172:function
155:function
470:Hashing
428:. 2016.
402:. 1994.
40:probing
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303:note 2
248:return
224:note 1
211:return
193:return
183:return
166:return
145:record
135:remove
127:lookup
162:while
30:, or
381:ISBN
342:The
290:else
255:loop
187:else
133:and
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229:set
149:var
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168:i
129:,
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344:O
337:O
329:i
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321:j
317:k
313:j
309:i
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