Results 1 
5 of
5
A Survey of Combinatorial Gray Codes
 SIAM Review
, 1996
"... The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing nbit binary numbers so that ..."
Abstract

Cited by 81 (2 self)
 Add to MetaCart
The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing nbit binary numbers so that successive numbers differ in exactly one bit position, as well as work in the 1960's and 70's on minimal change listings for other combinatorial families, including permutations and combinations. The area of combinatorial Gray codes was popularized by Herbert Wilf in his invited address at the SIAM Discrete Mathematics Conference in 1988 and his subsequent SIAM monograph in which he posed some open problems and variations on the theme. This resulted in much recent activity in the area and most of the problems posed by Wilf are now solved. In this paper, we survey the area of combinatorial Gray codes, describe recent results, variations, and trends, and highlight some open problems. ...
Generating Linear Extensions Fast
"... One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generate all of t ..."
Abstract

Cited by 36 (6 self)
 Add to MetaCart
One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generate all of the linear extensions of a poset in constant amortized time; that is, in time O(e(P)) , where e ( P ) =  E(P) . The fastest previously known algorithm for generating the linear extensions of a poset runs in time O(n e(P)) , where n is the number of elements of the poset. Our algorithm is the first constant amortized time algorithm for generating a ``naturally defined'' class of combinatorial objects for which the corresponding counting problem is #Pcomplete. Furthermore, we show that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions. The algorithm is practical and can be modified to efficiently count linear extensions, and to compute P(x < y) , for all pairs x,y , in time O( n^2 + e ( P )).
Generating Linear Extensions of Posets by Transpositions
 J. Combinatorial Theory (B
, 1992
"... This paper considers the problem of listing all linear extensions of a partial order so that successive extensions differ by the transposition of a single pair of elements. A necessary condition is given for the case when the partial order is a forest. A necessary and sufficient condition is given f ..."
Abstract

Cited by 27 (2 self)
 Add to MetaCart
This paper considers the problem of listing all linear extensions of a partial order so that successive extensions differ by the transposition of a single pair of elements. A necessary condition is given for the case when the partial order is a forest. A necessary and sufficient condition is given for the case where the partial order consists of disjoint chains. Some open problems are mentioned. 1 Introduction Many combinatorial objects can be represented by permutations subject to various restrictions. The set of linear extensions of a poset can be viewed as a set of permutations of the elements of the poset. If the Hasse diagram of the poset consists of two disjoint chains, then the linear extension permutations correspond to combinations. If the poset consists of disjoint chains, then the linear extension permutations correspond to multiset permutations. The extensions of the poset that is the product of a 2element chain with an nelement chain correspond to "ballot sequences" of ...
Generating Alternating Permutations Lexicographically
 BIT
, 1990
"... Abstract A permutation ss1ss2 \Delta \Delta \Delta ssn is alternating if ss1! ss2? ss3! ss4 \Delta \Delta \Delta. We present a constant averagetime algorithm for generating all alternating permutations in lexicographic order. Ranking and unranking algorithms are also derived. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract A permutation ss1ss2 \Delta \Delta \Delta ssn is alternating if ss1! ss2? ss3! ss4 \Delta \Delta \Delta. We present a constant averagetime algorithm for generating all alternating permutations in lexicographic order. Ranking and unranking algorithms are also derived.
Variations of Base Station Placement Problem on the Boundary of a Convex Region
"... Due to the recent growth in the demand of mobile communication services in several typical environments, the development of efficient systems for providing specialized services has become an important issue in mobile communication research. An important subproblem in this area is the basestation p ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Due to the recent growth in the demand of mobile communication services in several typical environments, the development of efficient systems for providing specialized services has become an important issue in mobile communication research. An important subproblem in this area is the basestation placement problem, where the objective is to identify the location for placing the basestations. Mobile terminals communicate with their respective nearest base station, and the base stations communicate with each other over scarce wireless channels in a multihop fashion by receiving and transmitting radio signals. Each base station emits signal periodically and all the mobile terminals within its range can identify it as its nearest base station after receiving such radio signal. Here the problem is to position the base stations such that each point in the entire area can communicate with at least one basestation, and total power required for all the basestations in the network is minimized. A different variation of this problem arises when some portions of the target region is not