Michael L. Fredman. Observations on the complexity of generating quasi-Gray codes. SIAM J. Comput., 7(2):134--146, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....combinations of updates and queries; a dash indicates lack of support for a particular operation. 5 Computational models. Our algorithms run on a random access machine with logarithmic word size and standard unit cost operations. The lower bounds are proved in the cell probe model of Fredman [21] and A.C. Yao [41] The model allows arbitrary operations on registers and can be regarded as a strong nonuniform version of the RAM, the cell size is denoted b = b(n) The model makes no assumptions on the preprocessing time or the size of the data structure. Nondeterminism. The worst case lower ....

Michael L. Fredman. Observations on the complexity of generating quasi-Gray codes. SIAM Journal on Computing, 7(2):134-146, 1978.

....1 shows an implementation for recomputing or n . It uses M [0] to store a counter of the number of 1s in x. The figure also indicates that it makes sense to explain our algorithms in English rather than by exhibiting cell probe implementations. Roots. The cell probe model was defined by Fredman [24] for constant cell size, but earlier Minsky and Papert [52, x 12.6] reason (about a static problem) within a model model that is essentially the same. Its most famous application 16 DYNAMIC COMPUTATION [1.3 is a paper of Yao [72] to whom the model is often attributed, e.g. by Ajtai [2] in (yet) ....

Michael L. Fredman. Observations on the complexity of generating quasiGray codes. SIAM Journal of Computing, 7(2):134--146, 1978.

....s) return x 1 Delta Delta Delta x i mod 2 provided that js Gamma P i j=1 x j j 1 (otherwise the behaviour of the query algorithm is undefined) Theorem 2 shows that this problem still requires Omega Gammaqui n= log log n) per operation. We reason within the cell probe model of Fredman [10] and Yao [27] with some extensions to cope with our stronger modes of computation. This can be viewed as a nonuniform version of the random access computer with arbitrary register instructions. Especially, our lower bounds are valid on random access machines with unit cost instructions on ....

....for completeness. We consider a specific sequence of operations that consists of a number of updates followed by a single query. The update sequence is chosen at random from a set U defined in Sect. 3.5. 3.1. Model of computation. The computational model is an extension of the cell probe model [10, 27]; since there is only a single query, which happens at the very end of the sequence, we can model query algorithms by nondeterministic decision trees. More precisely, a cell probe algorithm consists of a family of trees, one for each operation, and a memory M 2 f0; 2 b Gamma 1g . We ....

Michael L. Fredman. Observations on the complexity of generating quasi-Gray codes. SIAM Journal of Computing, 7(2):134--146, 1978.

....graph is the shuffle exchange network and a Hamilton path would be a Gray code for binary strings respecting this adjacency criterion. The existence of a Hamilton path in the shuffle exchange graph, a long standing open problem, was recently established by Feldman and Mysliwietz [FM93] In [Fre79], Fredman considers complexity issues involved in generating arbitrary subsets of the set of n bit strings so that successive strings differ only in one bit. He calls these quasi Gray codes and establishes bounds and trade offs on the resources required to generate successors using a decision ....

M. L. Fredman. Observations on the complexity of generating quasi-gray codes. SIAM Journal on Computing, 7(2):134--146, 1979.

....unique interval I for which j 2 I and returns min(I) The Split Find problem SPLIT FIND(n) is defined in the same way, except that union i operations are not allowed. In this paper, we consider implementing data types in the cell probe or decision assignment tree model, studied in several papers [2, 4, 8, 9, 10, 12, 18, 20, 24]. In this model, the complexity of a computation is the number of cells accessed in the random access memory containing the data structure during the computation, while the computation itself is for free. The number of bits b in a cell is a parameter of the model. For dynamic problem, like the ....

M.L. Fredman, Observations on the complexity of generating quasi-Gray codes, SIAM J. Comput. 7 (1978) 134-146.

....it as a subset of f0; 1g and consider its restriction n to f0; 1g n , i.e. we consider as a family of Boolean functions. The non uniform model in which we consider implementing this restricted problem is the cell probe or decision assignment tree model, previously considered by Fredman [7,8] and Fredman and Saks [9] In this model, the complexity of a computation is the number of cells accessed in the random access memory containing the data structure during the computation, while the computation itself is for free (and information about which operation to perform is also given for ....

M.L. Fredman, "Observations on the Complexity of Generating quasi-Gray Codes," SIAM Journal on Computing 7 (1978), 134--146.

....query algorithm receives almost the correct answer for free. The updates are as before, and the query is the behaviour of the query algorithm is undefined) Theorem 2 shows that this problem still requires#qui n log log n) per operation. We reason within the cell probe model of Fredman [10] and Yao [28] with some extensions to cope with our stronger modes of computation. This can be viewed as a nonuniform version of the random access computer with arbitrary register instructions. Especially, our lower bounds are valid on random access machines with unit cost instructions on ....

....3 Proof of Theorem 1 We consider a specific sequence of operations that consists of a number of updates followed by a single query. The update sequence is chosen at random from a set U defined in Sect. 3.5. 3.1 Model of computation. The computational model is an extension of the cell probe model [10, 28]; since there is only a single query in the hard sequence of operations constructed in our proof, which happens at the very end of the sequence, we can model query algorithms by nondeterministic decision trees. More precisely, a cell probe algorithm consists of a family of trees, one for each ....

Michael L. Fredman. Observations on the complexity of generating quasi-Gray codes. SIAM J. Comput., 7(2):134--146, 1978.

No context found.

M.L. Fredman, Observations on the complexity of generating quasi-Gray codes, SIAM Journal of Computing, 7:134--146, 1978.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC