Topic
Combinatorial method
About: Combinatorial method is a research topic. Over the lifetime, 100 publications have been published within this topic receiving 2410 citations.
Papers published on a yearly basis
Papers
TL;DR: The area of combinatorial Gray codes is surveyed, recent results, variations, and trends are described, and some open problems are highlighted.
Abstract: 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 n-bit binary numbers so that successive numbers differ in exactly one bit position, as well as work in the 1960s and 1970s 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 Conference on Discrete Mathematics in 1988 and his subsequent SIAM monograph [Combinatorial Algorithms: An Update, 1989] 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.
559 citations
TL;DR: The photophysical properties of the resulting transition-metal-based chromophores were compared against a series of analogous, traditionally prepared species and the strong overlap between these two sets confirms the identity of the parallel synthesis products and supports the truthfulness of the combinatorial results.
Abstract: A method for accelerating the discovery of ionic luminophores using combinatorial techniques is reported. The photophysical properties of the resulting transition-metal-based chromophores were compared against a series of analogous, traditionally prepared species. The strong overlap between these two sets confirms the identity of the parallel synthesis products and supports the truthfulness of the combinatorial results. Further support for the combinatorial method comes from the adherence of these complexes to the energy gap law. The relationship between the structure of a complex and its photophysical properties was also considered, and static DFT calculations were used to assess whether it is feasible to predict the luminescent behavior of novel materials.
512 citations
TL;DR: Algorithm MSG generates the maximal structure (super-structure) of a process synthesis problem; it can also be the basic algorithm in generating a mathematical programming model for this problem and leads to additional combinatorial algorithms of process synthesis including those for decomposition and for accelerating branch and bound search.
224 citations
TL;DR: Computational experiments comparing the resulting branch-and-price method to competing methodologies in the literature are presented and suggest that the technique yields a significant improvement on the hard instances of this problem.
124 citations
TL;DR: In this paper, the optimal control performance of a single signal-controlled junction is investigated and two existing methods for analysing this control problem are discussed, one of which is a combinatorial method, which generates all possible control structures in terms of groupings of streams of traffic to have green together and the order in which right of way is granted.
Abstract: The optimal control performance of a single signal-controlled junction is investigated. Two existing methods for analysing this control problem are discussed. One of these, a combinatorial method, generates all possible control structures in terms of groupings of streams of traffic to have green together and the order in which right of way is granted. The other method allows an existing control structure to be optimised by convex programming techniques. Incompatibilities between these two approaches are illustrated and it is shown that they cannot be combined in a satisfactory manner. A new procedure is framed that allows a control structure generated by the combinatorial method to be optimised directly. This procedure is applied to an example junction to illustrate its use.
102 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2024 | 2 |
| 2023 | 1 |
| 2022 | 6 |
| 2021 | 2 |
| 2020 | 5 |
| 2019 | 2 |