R. E. Tarjan, "A Class of Algorithms That Require Nonlinear Time to Maintain Disjoint Sets", J. Comput. and Sys. Sci., 18 (1979) 110--127. 10  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... programming languages according to schematology , as introduced by Paterson and Hewitt [9] The first use of schematology for a comparison based on complexity rather than computability is due to Pippenger [10] The special case of atomic symbols, in the sense used here, was considered by Tarjan [13]. The restriction to on line computation is well established in the literature of automata theory; see Hennie [4] We should say a few words about the models we use to embody the powers of pure and impure Lisp. These models will be the pure and impure Lisp machines. Such a machine will be ....

R. E. Tarjan, "A Class of Algorithms That Require Nonlinear Time to Maintain Disjoint Sets", J. Comput. and Sys. Sci., 18 (1979) 110--127. 10

....a query time of O(t=B log c B n) where t is the number of points to be reported and c is a constant, can only be achieved at the expense of Omega Gamma n=B) log n= log log B n) disk blocks of storage. The external memory pointer machine is a natural generalization of the pointer machine model [33] and is suitable for analyzing secondary memory algorithms. Our lower bound shows that we cannot implement an efficient data structure for 2 dimensional range searching in external memory using O(n log n=B log log n) disk blocks of storage. Thus in order to perform 2 dimensional range searching in ....

....that that answers rectangular queries with the worst case efficiency of O(log c B n t=B) I O s, must use Omega Gamma n B log( n B ) log log B n) disk blocks of storage. Our model of computation called the external memory pointer machine is a natural generalization of a pointer machine [33], and is suitable for analyzing external memory algorithms. We model our data structure as a directed graph G = V; E) with a source node s. Each node of the graph corresponds to a disk block of memory and is allowed to have B data and pointer fields. In this way, the external memory can be ....

R. E. Tarjan, "A Class of Algorithms that Require Nonlinear Time to Maintain Disjoint Sets," JCSS 18 (1979), 110--127.

....Corollary 4.5 are asymptotically optimal for a large alphabet Sigma whose characters can only be accessed by comparisons. We prove the lower bound for the Prefix Search(P ) operation by using the external memory pointer machine, introduced in [42] with the aim of generalizing the pointer machine [43] to external memory. This also holds for Range Query and Substring Search operations. In the externalmemory pointer machine, a data structure is seen as a graph with a source vertex s. Each vertex is a disk page of size B, which contains no more than B items (i.e. characters, polynomially bounded ....

Tarjan, R. A class of algorithms that require nonlinear time to maintain disjoint sets. Journal of Computer and System Science 18 (1979), 110--127.

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