A Parallel Solution to the Extended Set Union Problem with Unlimited Backtracking
نویسندگان
چکیده
In this paper, we study on the EREW-PRAM model a parallel solution to the extended set union problem with unlimited backtracking which maintains a dynamic partition Π of an n-element set S subject to the usual operations Find, Union, Backtrack and Restore as well as the new operations SetUnion, MultiUnion. The SetUnion operation is a special case of the commonly known Union operation aimed to unify two prespecified set-names, while MultiUnion operation deals with a batch of Union operations. A new data structure, called k-Parallel Union Find (or, k-PUF) trees, is introduced to represent a disjoint set in Π. The structure is defined for a wide range for the parameter k, but the more interesting results are achieved for k = logn log logn . In this case, using thek-PUF trees, both SetUnion and Restore operations are performed in constant parallel time requiring optimal work O(k). This constant-time performance is not achievable parallelizing the existing data structures. Moreover, using p = O(k) processors, MultiUnion for a batch of p operations is performed in O(k) time, requiring optimal work O(pk).
منابع مشابه
The Set Union Problem With Unlimited Backtracking
An extension of the disjoint set union problem is considered, where the extra primitive backtrack(i) can undo the last i unions not yet undone. Let n be the total number of elements in all the sets. A data structure is presented that supports each union and find in O(lognj loglogn) worst-case time and each backtrack(i) in 0(1) worst-case time, irrespective of i. The total space required by the ...
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