Lining up in random order offers a good chance of getting everyone aboard in time proportional to the square root of N. Under this regime the total boarding time is proportional to N, the total number of passengers. Then, everyone forward of row 28 has to wait for the next six people to sort themselves out. The problem is that no one in rows 1 through 28 can reach their row until at least some of the six passengers in row 29 seat themselves. Boarding should be a completely orderly process, with everyone sitting down after the minimum possible delay, no? No. Suppose further that the last-first policy can be enforced perfectly, so that all the passengers in row 29 are first in line, followed by those in row 28, and so on. Suppose there are 29 rows of seats with six seats per row, and the flight is full. The geometric context of the problem turns out to be a two-dimensional spacetime with a Lorentz metric there’s a combinatorial element to the story, involving longest increasing subsequences from there, I’m afraid it gets even deeper, and at one point we find ourselves dealing with “the normalized discrepancy of the largest eigenvalue of an N x N matrix in the Gaussian unitary ensemble (GUE).”įor all that, the ultimate outcome is clear enough, and it even makes intuitive sense. The authors call forth quite a dazzling array of high-powered mathematical tools in the course of their analysis. The paper, posted in the physics division of the arXiv, is by Eitan Bachmat, Daniel Berend, Luba Sapir and Natan Stolyarov (all of Ben-Gurion University) and Steven Skiena of the State University of New York at Stony Brook. We might be better off lining up in random order. The airlines’ last-shall-be-first strategy doesn’t work. By filling the airplane from back to front, the theory goes, passengers sitting in the rear won’t have to wait in the aisle while the couple in 8-A and 8-B stow their luggage, fetch blankets and pillows, argue over who gets the window, settle into their seats, get up again to retrieve a book from the overhead bin, and then discover that their tickets are actually for 18 A and B.Ī recent paper reveals the awful truth. My boarding pass is for seat 14B.įrequent flyers understand the rationale behind this routine. Ten minutes later they called for rows 20 to 29. “Passengers in rows 25 to 29 are invited to board the aircraft” was the first announcement. The first-class plutocrats are already aboard, and now the rest of us are filing on, one section at a time. The flight is late and overbooked there’s a crowd of hopeful standbys at the podium. I am at gate C21 at Houston Intercontinental, en route to San Antonio.
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