Searching for something you have found once before, is a very bad solution.
It is like catching a fish and then throwing it back into the ocean and attempting to find that same fish, again.
Real example that happened to me this week. I had mentioned this research in a post but did not include a link to it. I didn’t remember the names of the researchers or their location.
From the news bulletin:
Whether sudoku, a map of Germany or solid bodies – in all of these cases, it’s all about counting possibilities. In the sudoku, it is the permitted solutions; in the solid body, it is the possible arrangements of atoms. In the map, the question is how many ways the map can be colored so that adjacent countries are always shown in a different color. Scientists depict these counting problems as a network of lines and nodes. Consequently, they need to answer just one question: How many different ways are there to color in the nodes with a certain number of colors? The only condition: nodes joined by a line may not have the same color. Depending on the application, the color of a node is given a completely new significance. In the case of the map, “color” actually means color; with sudoku the “colors” represent different figures.
“The existing algorithm copies the whole network for each stage of the calculation and only changes one aspect of it each time,” explains Frank van Bussel of the Max Planck Institute for Dynamics and Self-Organization (MPIDS). Increasing the number of nodes dramatically increases the calculation time. For a square lattice the size of a chess board, this is estimated to be many billions of years. The new algorithm developed by the Göttingen-based scientists is significantly faster. “Our calculation for the chess board lattice only takes seven seconds,” explains Denny Fliegner from MPIDS.
Without naming the search engine, would you believe that:
network +color +node
results in 24 “hits,” none of which are the research in question.
Remembering some of the terms in the actual scholarly article I searched using:
"chromatic polynomials" +network
Which resulted in three (3) scholarly articles and one “hit,” none of which were the research in question.
As you may suspect, variations on these searches resulted in similar “non-helpful” results.
I had not imagined the research in question but searching was unable to recover the reference.
Well, using a search engine was unable to recover the reference.
Knowing that I had bookmarked the site, I had to scan a large bookmark file for the likely entry.
Found it and so I don’t have to repeat this non-productive behavior, what follows are the citations and some text from each to help with the finding, next time.
The general news article:
How many different sudokus are there? How many different ways are there to color in the countries on a map? And how do atoms behave in a solid? Researchers at the Max Planck Institute for Dynamics and Self-Organization in Göttingen and at Cornell University (Ithaca, USA) have now developed a new method that quickly provides an answer to these questions. In principle, there has always been a way to solve them. However, computers were unable to find the solution as the calculations took too long. With the new method, the scientists look at separate sections of the problem and work through them one at a time. Up to now, each stage of the calculation has involved the whole map or the whole sudoku. The answers to many problems in physics, mathematics and computer science can be provided in this way for the first time. (New Journal of Physics, February 4, 2009)
The New Journal of Physics article:
Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions by Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg.
Abstract:
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.
GENERAL SCIENTIFIC SUMMARY
Introduction and background. The number of accessible states of a complex physical system fundamentally impacts its static and dynamic properties. For instance, antiferromagnets often exhibit an exponential number of energetically equivalent ground states and thus positive entropy at zero temperature – an exception to the third law of thermodynamics. However, counting the number of ground states, such as for the Potts model antiferromagnet, is computationally very hard (so-called sharp-P hard), i.e. the computation time generally increases exponentially with the size of the system. Standard computational counting methods that use theorems of graph theory are therefore mostly restricted to very simple or very small lattices.
Main results. Here we present a novel general-purpose method for counting. It relies on a symbolic algorithm that is based on the original physical representation of a Potts partition function and is implemented in the computer algebra language FORM that was successfully used before in precision high-energy physics.
Wider implications. The bottom-up nature of the algorithm, together with the purely symbolic implementation make the new method many orders of magnitude faster than standard methods. It now enables exact solutions of various systems that have been thus far computationally inaccessible, including lattices in three dimensions. Through the relation of the Potts partition functions to universal functions in graph theory, this new method may also help to access related counting problems in communication theory, graph theory and computer science.
The language used was FORM.
This search reminded me that maps are composed of found and identified things.
Which explains the difference between searching the WWW versus a map of found things.