Recent News

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Happy -1+(2/.3)*45*6.78-9

(hint: 2/.3 times 45 times 6.78 is 2034)

(I guess I'm gettin' kinda old: 12.3+.4-5.6+78.9; think of Maxwell Smart. In fact, I've now lived more than 31415.9265 days.)

Happy Π Day

In honor of March 14, I've written an “unpublication” about combinatorial patterns called parades, which I think are loads of fun. Take a look!

Sorry: No rewards are given for errors that people find in unpublications. But of course I always welcome your feedback.

TAOCP update

The fourth volume of The Art of Computer Programming deals with Combinatorial Algorithms, the area of computer science where nonobvious techniques have the most dramatic effects. I love it the most, because one good idea can often make a program run a million times faster. It's a huge, fascinating subject, and Part 1 (Volume 4A, 883 pages, now in its twenty-third printing) was published in 2011; Part 2 (Volume 4B, 714 pages, now in its second printing) was published at the close of 2022. I'm hoping to make the first 250 or so pages of Volume 4C available this year, in preliminary paperback format.

While preparing many of the new exercises in Volume 4B, I spent a lot of time attempting to improve on expositions that I found in the literature. And in several noteworthy cases, nobody has yet pointed out any errors. It would be nice to believe that I actually got the details right on my first attempt; but that seems unlikely, because I had hundreds of chances to make mistakes. So I fear that the most probable hypothesis is that nobody has been sufficiently motivated to check the finer points out carefully as yet.

I still cling to a belief that such details are extremely instructive. Thus I would like to enter here a plea for some readers to tell me explicitly, “Dear Don, I have read exercise N and its answer very carefully, and I believe that it is 100% correct,” where N is one of the following exercise numbers:

• MPR-28-29: Prove basic inequalities for sums of independent binary random variables
• MPR-50: Prove that Ross's conditional expectation inequality is sharper than the second moment inequality
• MPR-59: Derive the four functions theorem
• MPR-61: Show that independent binary random variables satisfy the FKG inequality
• MPR-99: Generalize the Karp–Upfal–Wigderson bound on expected loop iterations
• MPR-103-104: Study ternary “coupling from the past”
• MPR-121-122: Study the Kullback–Leibler divergence of one random variable from another
• MPR-127: Analyze the XOR of independent sparse binary vectors
• MPR-130-131: Derive paradoxical facts about the Cauchy distribution (which has “heavy tails”)
• 7.2.2-79: Analyze the sounds that are playable on the pipe organ in my home
• 7.2.2.1-29-30: Characterize all search trees that can arise with Algorithm X
• 7.2.2.1-55: Determine the fewest clues needed to force highly symmetric sudoku solutions
• 7.2.2.1-104: Construct infinitely many “perfect” n-tone rows
• 7.2.2.1-121: Determine which of the 92 Wang tiles in exercise 2.3.4.3–5 can actually be used when tiling the whole plane
• 7.2.2.1-129: Enumerate all the symmetrical solutions to MacMahon's triangle-tiling problem
• 7.2.2.1-147: Construct all of the “bricks” that can be made with MacMahon's 30 six-colored cubes
• 7.2.2.1-151-152: Arrange all of the path dominoes into a single loop
• 7.2.2.1-196: Analyze the running time of Algorithm X on bounded permutation problems
• 7.2.2.1-262: Study the ZDDs for domino and diamond tilings that tend to have large “frozen” regions
• 7.2.2.1-305-306: Find optimum arrangements of the windmill dominoes
• 7.2.2.1-320: Find all ways to make a convex shape from the fourteen tetraboloes
• 7.2.2.1-323: Find all ways to make a skewed rectangle from the ten tetraskews
• 7.2.2.1-334: Build fake solutions for Soma-cube shapes
• 7.2.2.1-337: Design a puzzle that makes several kinds of “dice” from the same bent tricubes
• 7.2.2.1-346: Pack space optimally with small tripods
• 7.2.2.1-375: Determine the smallest incomparable dissections of rectangles into rectangles
• 7.2.2.1-387: Classify the types of symmetry that a polycube might have
• 7.2.2.1-432: Find the most interesting 3×3 kakuro puzzles
• 7.2.2.1-442: Enumerate all hitori covers of small grids
• 7.2.2.2-6: Verify a certain (previously unpublished) lower bound on van der Waerden numbers W(3,k)
• 7.2.2.2-57: Find a 6-gate way to match a certain 20-variable Boolean function at 32 given points
• 7.2.2.2-165: Devise an algorithm to compute the largest positive autarky of given clauses
• 7.2.2.2-212: Prove that partial latin square construction is NP-complete
• 7.2.2.2-282: Find a linear certificate of unsatisfiability for the flower snark clauses
• 7.2.2.2-306-308: Study the reluctant doubling strategy of Luby, Sinclair, and Zuckerman
• 7.2.2.2-318: Find the best possible Local Lemma for d-regular dependency graphs with equal weights
• 7.2.2.2-322: Show that random-walk methods cannot always find solutions of locally feasible problems using independent random variables
• 7.2.2.2-335: Express the Möbius series of a cocomparability graph as a determinant
• 7.2.2.2-339: Relate generating functions for traces to generating functions for pyramids
• 7.2.2.2-347: Find the best possible Local Lemma for a given chordal graph with arbitrary weights
• 7.2.2.2-356: Prove the Clique Local Lemma
• 7.2.2.2-363: Study the stable partial assignments of a satisfiability problem
• 7.2.2.2-442-444: Study the UC and PC hierarchy of progressively harder sets of clauses
• 7.2.2.2-518: Reduce 3SAT to testing the permanent of a {-1,0,1,2} matrix for zero

Please don't be alarmed by the highly technical nature of these examples; more than 500 of the other exercises are completely non-scary, indeed quite elementary. But of course I do want to go into high-level details also, for the benefit of advanced readers. And those darker corners of my books are naturally the most difficult to get right. Hence this plea for help.

Remember that you don't have to work the exercise first. You're allowed to peek at the answer; in fact, you're even encouraged to do so. Please send success reports to the usual address for bug reports (taocp@cs.stanford.edu). Thanks in advance!

By the way, if you want to receive a reward check for discovering an error in TAOCP, your best strategy may well be to scrutinize the answers to the exercises that are listed above.

Preliminary sketches of material that will be in later parts of Volume 4C have also been drafted, and courageous readers who have nothing better to do might dare to take a peek at the comparatively raw copy in these “prefascicles.” One can look, for instance, at Pre-Fascicle 8a (Hamiltonian Paths and Cycles); Pre-Fascicle 9b (A Potpourri of Puzzles). Thanks to Tom Rokicki, those PostScript files are now searchable!

Oral histories

I seem to get older every day, and people keep asking me to reminisce about the glorious days of yore. If you're interested in checking out some of those videos and other archives, take a look at my news page for 2020, which I've updated with a few items captured after that year.

Public lectures in 2024

Although I must stay home most of the time and work on yet more books that I've promised to complete, I do occasionally get into speaking mode.

Saturday, January 6, 4pm to 5pm, in San Francisco (Moscone Center Room 024)

An invited talk, “Recreational Computer Science,” at the Joint Mathematics Meetings [JMM 2024] [due to a clerical error, this talk was given an incorrect title in the official program] (view the slides)

Wednesday, June 5, 8pm, in the MIT Samberg Conference Center

“Bijections”, the banquet talk at Richard Stanley's 80th birthday conference (view the slides) (watch the video)

Wednesday, August 14, 6pm Argentina time (+3 GMT)

All Questions Answered (via Zoom), as part of the “50th Latin American Computing Conference”, hosted by Universidad Nacional Del Sur in Bahia Blanca, Argentina (watch the video)

Thursday, October 24, 16:50 CEST (7:50am Pacific Daylight Time)

All Questions Answered (via Zoom), as part of the conference “Grapholinguistics in the 21st Century, 2024” to be held in Venice

Don Knuth's home page