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UnionFind with Constant Time Deletions
"... A unionfind data structure maintains a collection of disjoint sets under makeset, union and find operations. Kaplan, Shafrir and Tarjan [SODA 2002] designed data structures for an extension of the unionfind problem in which elements of the sets maintained may be deleted. The cost of a delete opera ..."
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Cited by 6 (1 self)
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structure that supports delete, aswell as makeset and union, operations in constant time, while still supporting find operations in O(log n) worstcase time and O(α(n)) amortized time, where n is the number of elements in the set returned by the find operation, and α(n) is a functional inverse of Ackermann
Meldable Heaps and Boolean UnionFind (Extended Abstract)
, 2002
"... In the classical meldable heap data type we maintain an itemdisjoint collection of heaps under the operations findmin, insert, delete, decreasekey, and meld. In the usual definition decreasekey and delete get the item and the heap containing it as parameters. We consider the modified problem whe ..."
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where decreasekey and delete get only the item but not the heap containing it. We show that for this problem one of the operations findmin, decreasekey, or meld must take nonconstant time. This is in contrast with the original data type in which data structures supporting all these three operations
The UnionFind Problem Is Linear
"... This paper has an error and has been retracted. It should simply be deleted from Citeseer. Baring that, I am submitting this "correction".
The unionfind problem, also known as the disjoint set union problem, involves two operations, union and find, on a collection of disjoint sets. Th ..."
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This paper has an error and has been retracted. It should simply be deleted from Citeseer. Baring that, I am submitting this "correction".
The unionfind problem, also known as the disjoint set union problem, involves two operations, union and find, on a collection of disjoint sets
• UnionFind • Sorting
"... • There are positive constants c and n0 such that f(N) <=c g(N) when N> = n0 • The growth rate of f(N) is less than or equal to the growth rate of g(N) • g(N) is an upper bound on f(N) • Example – Let f(N) = 2N2. Then • f(N) = O(N4) • f(N) = O(N3) • f(N) = O(N2) (best answer, asymptoticall ..."
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• There are positive constants c and n0 such that f(N) <=c g(N) when N> = n0 • The growth rate of f(N) is less than or equal to the growth rate of g(N) • g(N) is an upper bound on f(N) • Example – Let f(N) = 2N2. Then • f(N) = O(N4) • f(N) = O(N3) • f(N) = O(N2) (best answer
Interprocedural dataflow analysis via graph reachability
, 1994
"... The paper shows how a large class of interprocedural dataflowanalysis problems can be solved precisely in polynomial time by transforming them into a special kind of graphreachability problem. The only restrictions are that the set of dataflow facts must be a finite set, and that the dataflow fun ..."
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Cited by 454 (34 self)
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. In addition, the class of problems that our techniques handle includes many nonseparable problems, including trulylive variables, copy constant propagation, and possiblyuninitialized variables. Results are reported from a preliminary experimental study of C programs (for the problem of finding possibly
Selfadjusting binary search trees
, 1985
"... The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an am ..."
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Cited by 432 (18 self)
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The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have
Efficiency of a Good But Not Linear Set Union Algorithm
, 1975
"... Two types of instructmns for mampulating a family of disjoint sets which partitmn a umverse of n elements are considered FIND(x) computes the name of the (unique) set containing element x UNION(A, B, C) combines sets A and B into a new set named C. A known algorithm for implementing sequences of the ..."
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Cited by 321 (15 self)
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of these mstructmns is examined It is shown that, if t(m, n) as the maximum time reqmred by a sequence of m> n FINDs and n 1 intermixed UNIONs, then kima(m, n) _~ t(m, n) < k:ma(m, n) for some positive constants ki and k2, where a(m, n) is related to a functional inverse of Ackermann's functmn
QuasiLinearTime Algorithms by Generalisation of UnionFind in CHR
"... www.informatik.uniulm.de/pm/mitarbeiter/fruehwirth/ Abstract. The unionfind algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing the approp ..."
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Cited by 1 (0 self)
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www.informatik.uniulm.de/pm/mitarbeiter/fruehwirth/ Abstract. The unionfind algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing
A Simple and Efficient UnionFindDelete Algorithm
, 2010
"... The UnionFind data structure for maintaning disjoint sets is one of the best known and widespread data structures, in particular the version with constanttime Union and efficient Find. Recently, the question of how to handle deletions from the structure in an efficient manner has been taken up, fi ..."
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The UnionFind data structure for maintaning disjoint sets is one of the best known and widespread data structures, in particular the version with constanttime Union and efficient Find. Recently, the question of how to handle deletions from the structure in an efficient manner has been taken up
Deriving QuasiLinearTime Algorithms from UnionFind in CHR (Extended Abstract)
, 2006
"... The unionfind algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing the appropriate relations, we can derive fast algorithms for solving cer ..."
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The unionfind algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing the appropriate relations, we can derive fast algorithms for solving
Results 1  10
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