Reference Journey

Couple of days ago I wondered what will happen if I would trace back references of a randomly chosen OR paper. So, I selected article #7 from March/April 2012 issue of Operations Research journal and started investigating:

Jonathan Kluberg and Georgia Perakis, Generalized Quantity Competition for Multiple Products and Loss of Efficiency

Then I looked at reference #7:

Correa J. R., Schulz A. S., Stier-Moses N. E. (2004) Selfish routing in capacitated networks. Math. Oper. Res. 29(4):961–976

Then I looked at reference #7 of that paper:

Branston D. (1976) Link capacity functions: A review. Transportation Res. 10:223–236

I wanted to look at reference #6 of that paper: (reason for choosing 6 is that I could not access some papers reated with reference #7)

Braess D. (1968) Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12:258–268. (Full text link) – This paper is Braess’s paradox paper.

Reference #7 of that paper is

Pollack, M., und Wiebenson, W.: Solutions of the Shortest Route Problem  – A Review. Operation Research 8, 224-230 (1960)

Then:

GJ Minty, “A Comment on the Shortest-Route Problem,” Opns. Res. 5, 724 (1957)

Dantzig, George B., Disrete-Variable Extremum Problems. Operations Research. Apr57, Vol. 5 Issue 2, p266. 23p.

Harry M. Markowitz and Alan S. Manne, On the Solution of Discrete Programming Problems Econometrica
Vol. 25, No. 1 (Jan., 1957), pp. 84-110

G. Dantzig, R. Fulkerson and S. Johnson, Solution of a Large-Scale Traveling-Salesman Problem, Journal of the Operations Research Society of America Vol. 2, No. 4 (Nov., 1954), pp. 393-410

I think reading OR papers from 50’s is very helpful in understanding the basic of OR. Texts are not so complicated, and you can see how the problems originated, what were first attempts to solve them, what were the things authors could not try.

From Dantzig’s paper we go to this mathematics book:
W.  W.  R.  Ball,  Mathematical Recreations and Essays,  as  rev.  by  H.  S. M.  Coxeter,  11th  ed., Macmillan,  New  York,  1939. (Dantzig cites this book because of Hamiltonian game, so I looked at the references in Hamiltonian game section.)

Édouard Lucas Récréations mathématiques volume 2 page 215 is about Hamiltonian Game. The game is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a path such that every vertex is visited a single time, no edge is visited twice, and the ending point is the same as the starting point (Mathworld). It was invented by William Rowan Hamilton.

Twenty cities of the Hamiltonian Game:

On page 225 Lucas cites Cauchy’s article, I think that article is this. He tried to solve the game using geometry.

Cauchy cites Euclid’s elements. Euclid used Babylonian and Egyptian mathematics knowledge in his book.

We always say science is accumulation of knowledge, we stand on shoulders of giants. It was more powerful for me to observe this accumulation. I think by tracking back references we can rediscover contributions of forgotten scientists.

Similar trackbacking can be done by analyzing advisors. See example of Mike Trick.

Photo by VinothChandar