Philippe Flajolet Does Research. Smokes. Battles Administration. - - PowerPoint PPT Presentation

Philippe Flajolet

Does Research. Smokes. Battles Administration. Christian Konrad

Reykjavik University

December 12, 2014

Philippe Flajolet 1948 - 2011

Born: Dec. 1st, 1948 in Lyon Died: March 22nd, 2011 in Paris

July 4th, 2006

Philippe Flajolet: Short Description

2004

“Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do

• research. Smokes some more. Gives jobs to starving foreigners. Eats
• ccasionally.” — Eithne Murray

Luc Devroye on Philippe Flajolet

Luc Devroye, My friend, Gaz. Math. No. 129 (2011), 116-117.

July 4th, 2006

Luc Devroye on Philippe Flajolet

Luc Devroye, My friend, Gaz. Math. No. 129 (2011), 116-117. The image that is etched in my mind is that of Philippe Flajolet happily purring while listening to a great exposition by one of his students or col-

• leagues. At the first opportunity, he would shout something funny in the

direction of the speaker to show his appreciation. He was the community’s

• cheerleader. The inside of his car has never been cleaned, his hair cam-
• uflaged a biological experiment, his shirts were always untucked, and yet,

wherever he went, he was inevitably surrounded by friends and followers, admired for his brilliance and wit, and revered for his guidance and generos- ity.

Luc Devroye on Philippe Flajolet

Luc Devroye, My friend, Gaz. Math. No. 129 (2011), 116-117. ... he was a master of mathematical illustration. He liked to show that craft

• ff in his passionate talks, which grew more intense with every tick of the

clock, to end up in overtime. On one occasion, I saw the last button of his shirt pop off just before the final slide. [He started wearing Indian-style shirts above his belt in the last decade of his life to avoid such events.] One of his other passions was listening. His seminar series in Versailles was

• legendary. It was an honour to be invited. And Philippe listened, purred,

teased, shouted, applauded, and acted up - anything short of throwing a paper airplane at the speaker with a heart drawn on its wings. He was the glue that kept the community together.

Reactions About His Passing Away (1)

Luc Devroye: wrote on March 22, 2011: I do not care about the world

• today. Philippe Flajolet died this afternoon. My heart is in the gutter.

Why is it that the nicest, smartest, most generous guys have to go first? On Facebook: March 22, 2011—a day I will never forget. The world can go to hell. My friend, my brother, Philippe Flajolet just died. He was the guy I always wanted to be but never will be. Infinitely smart, generous, funny, radical, unconventional, creative, wonderful, wonderful, wonderful,.... Thank you Philippe.

Reactions About His Passing Away (2)

Bob Sedgewick and Wojtek Spankowski The world has lost a brilliant and productive mathematician. Philippe’s untimely passing means that many things may never be known. But his legacy is a coterie of followers passionately devoted to Philippe and his mathematics who will carry on. Our conferences will include a toast to Philippe, our research will build upon his work, our papers will include the inscription ’Dedicated to the memory of Philippe Flajolet’, and we will teach generations to come. Dear friend, we miss you so very much, but rest assured that your spirit will live on in our work.

Reactions About His Passing Away (3)

ALGO team webpage: Philippe Flajolet, our former Fearless Leader, died suddenly on March 22,

• 2011. Annus horribilis!

Our band, which was so merry, is now extremely sad, and we remained voiceless for a lot of time. But, we cannot forget our beloved Pifou and his eternally renewed interest for algorithmics, mathematics, and Indo-European linguistics; his taste for good wine and good food; his constant humor.

Short CV

1958 - 1966: Lyc´ ee Amp` ere in Lyon, Bac. 1968 - 1971: ´ Ecole Polytechnique de Paris 1971 - 2011: INRIA, Rocquencourt Recruited by Maurice Nivat 1976: Co-founder of the ALGO group (together with Jean Vuillemin) 1981: Head of the ALGO group 1972: PhD, Universit´ e Paris Diderot Advisors: Maurice Nivat, Jean Vuillemin 1979: Habilitation, Universit´ e Paris Sud

Short CV

´ Ecole Polytechnique

Short CV

1958 - 1966: Lyc´ ee Amp` ere in Lyon, Bac. 1968 - 1971: ´ Ecole Polytechnique de Paris 1971 - 2011: INRIA, Rocquencourt Recruited by Maurice Nivat 1976: Co-founder of the ALGO group (together with Jean Vuillemin) 1981: Head of the ALGO group 1972: PhD, Universit´ e Paris Diderot Advisors: Maurice Nivat, Jean Vuillemin 1979: Habilitation, Universit´ e Paris Sud

Short CV

INRIA Roquencourt

Short CV

1958 - 1966: Lyc´ ee Amp` ere in Lyon, Bac. 1968 - 1971: ´ Ecole Polytechnique de Paris 1971 - 2011: INRIA, Rocquencourt Recruited by Maurice Nivat 1976: Co-founder of the ALGO group (together with Jean Vuillemin) 1981: Head of the ALGO group 1972: PhD, Universit´ e Paris Diderot Advisors: Maurice Nivat, Jean Vuillemin 1979: Habilitation, Universit´ e Paris Sud

Doctoral Advisors

Research

“... a happy marriage between combinatorics and analysis applied to computer science and discrete mathematics.” Research Areas: Analytic Combinatorics (Average Case) Analysis of Algorithms Symbolic Computation Co-authored by Robert Sedgewick

Research

“... a happy marriage between combinatorics and analysis applied to computer science and discrete mathematics.” Research Areas: Analytic Combinatorics (Average Case) Analysis of Algorithms Symbolic Computation Co-authored by Robert Sedgewick

Robert Sedgewick

Robert Sedgewick: Data Movement in Odd-Even Merging. SIAM J.

• Comput. 7(3): 239-272 (1978)

2 ln 2 · Γ kπi ln 2

• ζ

2kπi ln 2

• Philippe Flajolet et al.: On the Average Number of Registers

Required for Evaluating Arithmetic Expressions. FOCS 1977: 196-205 2kπi − log ... log ... Γ kπi ln 2

• ζ

2kπi ln 2

Robert Sedgewick

Robert Sedgewick: Data Movement in Odd-Even Merging. SIAM J.

• Comput. 7(3): 239-272 (1978)

2 ln 2 · Γ kπi ln 2

• ζ

2kπi ln 2

• Philippe Flajolet et al.: On the Average Number of Registers

Required for Evaluating Arithmetic Expressions. FOCS 1977: 196-205 2kπi − log ... log ... Γ kπi ln 2

• ζ

2kπi ln 2

• I believe that we have a formula in common!

Analytic Combinatorics

“Determine properties of combinatorial configurations through an approach based extensively on analytic methods.” Example: In how many ways can we lay n items on a table, in a row?

Analytic Combinatorics

“Determine properties of combinatorial configurations through an approach based extensively on analytic methods.” Example: In how many ways can we lay n items on a table, in a row? Number of permutations of n elements n! = 1 · 2 · 3 . . . (n − 1) · n n! ≈ √ 2πn n e n . (Stirling’s Formula) Discovery of factorial function ∼ 500 B.C.

Analytic Combinatorics

“Determine properties of combinatorial configurations through an approach based extensively on analytic methods.” Example: In how many ways can we lay n items on a table, in a row? Number of permutations of n elements n! = 1 · 2 · 3 . . . (n − 1) · n n! ≈ √ 2πn n e n . (Stirling’s Formula) Discovery of factorial function ∼ 500 B.C. How many alternating permutations are there for n = 1, 3, 5, . . . ?

8 7 9 3 ր ց ր ց ր ց ր ց 4 6 5 1 2

Analytic Combinatorics

“Determine properties of combinatorial configurations through an approach based extensively on analytic methods.” Example: In how many ways can we lay n items on a table, in a row? Number of permutations of n elements n! = 1 · 2 · 3 . . . (n − 1) · n n! ≈ √ 2πn n e n . (Stirling’s Formula) Discovery of factorial function ∼ 500 B.C. How many alternating permutations are there for n = 1, 3, 5, . . . ?

8 7 9 3 ր ց ր ց ր ց ր ց 4 6 5 1 2 1 3 5 7 9 11 13

• alt. perm.

1 2 16 272 7936 353792 22368256 n! 1 6 120 5040 362880 39916800 6227020800

Analytic Combinatorics (2)

1, 2, 16, 272, 7936, 353792, 22368256, . . . D´ esir´ e Andr´ e’s Discovery (1881): Taylor expansion of tan z tan z = 1 z 1! + 2z3 3! + 16z5 5! + 272z7 7! + 7936z9 9! + 353792z11 11! + . . . tan z is a generating function of the sequence Symbolic Computation: Compute coeff. of Taylor expansion of tan z Can we get a closed formula for the coefficients?

Analytic Combinatorics (3)

Analytic Methods: Approximate tan z at its singularities ± 1

2π by “simple” function

Deduce coefficients from simple function

1 3 5 7 9 11 13 15

• Alt. Perm.

1 2 16 272 7936 353792 22368256 1903757312 Estimation 1 1 15 271 7935 353791 22368251 1903757267

Applications

Algorithm analysis by analyzing underlying combinatorial structure Research Areas and Interests: Sorting algorithms Pattern in trees Factorization of integers and polynomials on finite fields Birthday paradox Queuing theory Probabilistic counting Number of distinct elements . . .

Applications

Algorithm analysis by analyzing underlying combinatorial structure Research Areas and Interests: Sorting algorithms Patterns in trees Factorization of integers and polynomials on finite fields Birthday paradox, hashing Queuing theory Probabilistic counting Number of distinct elements . . .

Probabilistic Counting and Distinct Elements

Pioneer in the area of Streaming Algorithms: sequential access random access Perform a single pass over the data stream, use small memory Example: Read the totality of Shakespeare’s work, output: The number of words, The number of distinct words.

Streaming Algorithms

Streaming Algorithms: very active research area today Massive data set algorithms, when data access is expensive Data streams, e.g. statistics on a network router

Counting the Number of Words

Counting from 1 to n requires log n bits (information theoretic LB) How can we do it with fewer bits?

Counting the Number of Words

Counting from 1 to n requires log n bits (information theoretic LB) How can we do it with fewer bits? Approximate Counting: Compute k so that 2k ≤ n < 2k+1 n 1 2 3 4 5 6 7 8 . . . 15 16 k 1 1 2 2 2 2 3 . . . 3 4 2k 1 2 2 4 4 4 4 8 . . . 8 16

Counting the Number of Words

Counting from 1 to n requires log n bits (information theoretic LB) How can we do it with fewer bits? Approximate Counting: Compute k so that 2k ≤ n < 2k+1 n 1 2 3 4 5 6 7 8 . . . 15 16 k 1 1 2 2 2 2 3 . . . 3 4 2k 1 2 2 4 4 4 4 8 . . . 8 16 2-approximation Requires log log n bits!

Counting the Number of Words (2)

Algorithm by Robert Morris 1977, Bell Labs:

1 Initialize: k := 1 2 Increment: Do k = k + 1 with probability 2−k 3 Output: 2k − 2

First Full Analysis by Flajolet 1985: Expected value, Variance, . . . using generating functions

Number of Distinct Words

Number of Distinct Words: Whole of Shakespeare Trivial Approach: Store all distinct words Flajolet and Martin, 1985: Approximation 256 bytes of 4 bits each (= 128 bytes) Estimate 30897 against n = 28239 distinct words Note that 128 · 8 = 1024 ≪ 28239 (less than one bit per word)

Number of Distinct Words

Streaming Algorithms for Distinct Elements Problem: Flajolet and Martin, 1985 Cohen, 1997 Alon, Matias, Szegedy, 1999 (G¨

• del price 2005)

Gibbons, 2001 Gibbons, Tirthapura, 2001 Bar-Yossef, Jayram, Kumar, Sivakumar, Trevisan, 2002 Bar-Yossef, Kumar, Sivakumar, 2002 Indyk, Woodruff, 2003 Durand, Flajolet, 2003 Estan, Varghese, Fisk, 2006 Beyer, Haas, Reinwald, Sismanis, Gemulla, 2007 Flajolet, Fusy, Gandouet, Meunier, 2007 Brody, Chakrabarti, 2009 Kane, Nelon, Woodruff, 2010

Distinctions (1)

CNRS Silver Medal (2004) One gold medal per year, 15 silver medals per year, 40 bronze medals per year Member of the Acad´ emie des Sciences (2003) Member of the European Academy of Sciences Honorary Doctorate Degree: Brussels Univerity

Distinctions (2)

Chevalier de L´ egion d’honneur (July, 2010) Knight of the legion of honour Minimum 20 years of public service or 25 years of professional activity, and ”eminent merits” ”eminent merits”: Flawless performance of one’s trade as well as doing more than ordinarily expected, such as being creative and contributing to the growth of others. Knight 74 834 Officer 17 032 Commander 3 009 Grand Officer 314 Grand Cross 67 Grand Master 1

Distinctions (3)

1998: Special issue Algorithmica (journal) for his 50th birthday 2006: Discrete Mathematics (journal) lists Flajolet’s 1980 paper “Combinatorial Aspects of Continued Fractions” as one of the most influential papers since 1971 2008: Special issue Discrete Mathematics and Theoretical Computer Science for his 60th birthday S´ eminaire de Combinatoire Philippe Flajolet June 2011: Two conferences dedicated to Philippe Flajolet: ”Formal Power Series and Algebraic Combinatorics” and ”Analysis of Algorithms” Philippe Flajolet was very interested in linguistics, especially in

• Sanskrit. 2000 books of his own collection were donated to the

linguistics library in Paris and the new university library “Philippe Flajolet” in Versailles

Finally

Knuth Number: 1 Erd¨

• s Number: 2

Wiles Number: 4 Einstein Number: 6

That’s all folks!