J. T. Joichi, D. E. White, and S. G. Williamson, "Combinatorial Gray codes," IEEE SIAM J. Comput., vol. 9, pp. 130--141, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by identifying a changing place at any level of the tree, called the difference point, and the corresponding changing position down the tree, called the solution point. The concept of this paper can be viewed as a refinement of combinatorial Gray code introduced in Joichi, White and Williamson [19], Wilf [3] and Savage [4] which is in turn a generalization of the generation of binary reflected Gray code [20] Based on this approach, we derive a new O(1) time algorithm for generating parenthesis strings in an order different from that in [11] and an in place algorithm for generating ....

....first define the characteristic sequence of a parenthesis string a = a 1 . a n such that a i is the number of right parentheses between the i th and (i 1)th left parentheses for i n and a n is the number of right parentheses after the n th left parenthesis. This characerization is due to [9] and [19]. Example 1. For ( its characteristic sequence is given by (1, 1, 0, 2) Let the sum s be defined by s i = a 1 . a i for i=0, n, where s 0 = 0. Then s n =n and a can take the values 0, 1, i s i 1 , which are called valid values. Note that a n = n s n 1 . Based on ....

Joichi, J.T., D.E. White, and S.G. Williamson, Combinatorial Gray codes, SIAM Jour. Comput., 9 (1980) 130-141.

....mapping is a bijection between S(n) and R(n) 8] p. 18 19) For n = 4, the bijection is illustrated in the first two columns of Figure 1. A Gray code for a combinatorial family is a listing of the objects in the family so that successive objects differ in some pre specified, usually small, way [3]. Although any listing algorithm for one of S(n) or R(n) can be used for the other, small changes between objects of one family may be magnified by the bijection. For example, the partitions 1 = f1; 2; 5g; f3; 6g; f4g and 2 = f1; 3; 6g; f2; 5g; f4g differ only in that element 1 changes sets. ....

J. T. Joichi, D. E. White, and S. G. Williamson, "Combinatorial Gray codes," SIAM Journal on Computing 9, No. 1 (1980) 130-141. 11

....of mathematics can be posed as Gray code problems. Finally, and perhaps one of the main attractions of the area, Gray codes typically involve elegant recursive constructions which provide new insights into the structure of combinatorial families. The term combinatorial Gray code first appeared in [JWW80] and is now used to refer to any method for generating combinatorial objects so that successive objects differ in some pre specified, usually small, way. However, the origins of minimal change listings can be found in the early work of Gray [Gra53] Wells [Wel61] Trotter [Tro62] Johnson [Joh63] ....

....are hamiltonian. For many Gray code problems, especially those involving permutations, the associated graph is a Cayley graph. Although many Gray code schemes seem to require strategies tailored to the problem at hand, a few general techniques and unifying structures have emerged. The paper [JWW80] considers families of combinatorial objects, whose size is defined by a recurrence of a particular form, and some general results are obtained about constructing Gray codes for these families. Ruskey shows in [Rus92] that certain Gray code listing problems can be viewed as special cases of the ....

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J. T. Joichi, Dennis E. White, and S. G. Williamson. Combinatorial Gray codes. SIAM Journal on Computing, 9(1):130--141, 1980.

....algorithms are sometimes called combinatorial Gray codes (see Joichi, White, Research supported by the Natural Sciences and Engineering Research Council of Canada under grant A3379. y Partially supported by the Office of Naval research under contract N 00014 860419. and Williamson [4]) For binary trees, Gray code type generation has been considered by Proskurowski and Ruskey [11] Lucas [8] and Roelants and Ruskey [19] Let T(n) denote the set of all bitstrings with n zeros and n ones characterized by the prefix property (i.e. such that no prefix contains more 0 s than ....

J.T. Joichi, D.E. White, and S.G. Williamson. Combinatorial gray codes. SIAM J. Computing, 9:130--141, 1980.

....right rotation at node x. Our approach to the problem uses the paradigm of attaching alternating directions to elements or positions of the object in order to obtain Gray codes of combinatorial objects; see Proskurowski and Ruskey [12] Nijenhuis and Wilf [9] or Joichi, White, and Williamson [3] for examples. The rotation graph G n has vertex set consisting of all binary trees with n nodes. Two vertices are connected by an edge if a single left or right rotation will transform one tree into the other. This graph was used by Pallo [10] who showed that the directed version obtained by ....

J.T. Joichi, D.E. White, and S.G. Williamson. Combinatorial Gray codes. SIAM J. Computing, 9:130--141, 1980.

....) then the algorithm is said to run in linear amortized time. A constant amortized time algorithm is said to be loopless (or constant worst case time) if the amount of computation between successive objects is O(1) Examples of loopless algorithms may be found in Joichi, White, and Williamson [11], Dershowitz [4] and Ehrlich [5] The algorithm of Ruskey [17] for generating the ideals of a tree poset runs in linear amortized time. A constant amortized time algorithm for generating the ideals of bounded size of a tree poset was described by Beyer and Ruskey [2] The algorithm of Steiner ....

J.T. Joichi, D.E. White, and S.G. Willamson, "Combinatorial Gray Codes," SIAM J. Computing, 9 (1980) 130-141.

No context found.

J. T. Joichi, D. E. White, and S. G. Williamson, "Combinatorial Gray codes," IEEE SIAM J. Comput., vol. 9, pp. 130--141, 1980.

No context found.

J. T. Joichi, D. E. White and S. G. Williamson, Combinatorial Gray codes, SIAM J. Comput., 9 (1980), 130-141.

No context found.

J.T. Joichi, D.E. White, and S.G. Willamson, "Combinatorial Gray Codes," SIAM J. Computing, 9 (1980) 130-141.

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