About

Alan Siegel is a researcher with a focus on various areas in mathematics and computer science, including plane geometry, probability, and the mathematical analysis of hashing functions. His work involves resolving area optimization questions about polygons and related figures, providing intuitive proofs of classical geometric inequalities such as the isoperimetric inequality in the plane, and exploring arrangements of segments and the areas they encompass. Siegel has contributed to the understanding of performance analyses for closed hashing in models supporting real computation, as well as the theory of fast hash functions, universal classes of hash functions, and their time-space tradeoffs. In addition to his geometric and algorithmic research, Siegel has addressed probabilistic bounds, including medians of discrete random variables and Chernoff-Hoeffding bounds for sums of dependent and heterogeneously distributed random variables. His work often involves establishing bounds and inequalities with applications in probabilistic algorithms and processes. Overall, his research combines geometric, probabilistic, and computational perspectives to advance theoretical understanding in these interconnected fields.

Research topics

• Computer science
• Mathematics
• Algorithm
• Theoretical computer science
• Combinatorics

Selected publications

• Rebranding John Jay College: Adapting to an evolving higher education market

  Journal of brand strategy · 2017-12-01

  article1st authorCorresponding

  Institutions of higher education face an increasingly complicated business environment today, marked by slowing enrolments, rapidly inflating tuition fees and heightened competition for enrolment on- and offline. So it is no surprise that college presidents are paying more attention to branding and marketing, often turning to unified brand identity programmes to combat these forces. An authentic ‘brand identity’ requires both the organisation and the consumer to believe in what an institution stands for, and when that is achieved a loyal relationship is formed. The recent case of the rebranding for John Jay College of Criminal Justice in New York City provides an illustrative primer explaining how to go about such efforts and what to expect from a comprehensive rebrand.

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• An Interview with Philip Howard

  Design Management Review · 2012-05-22

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  Hundreds of pages of regulations didn't stop Enron, and they don't stop tax cheats either. Why not redesign the law to make the most of individual judgment and collective common sense?

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• Lower Bounds on Communication Complexity in VLSI

  2011-08-31 · 1 citations

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• Experiments in teaching an engaging and demystifying introduction to algorithms: Installment 1: Huffman Codes

  2009-01-01 · 7 citations

  articleOpen access1st authorCorresponding

  As is well known -- the Huffman algorithm is a remarkably simple, and is a wonderfully illustrative example of the greedy method in algorithm design. However, the Huffman problem, which is to design an optimal binary character code (or an optimal binary tree with weighted leaves) is intrinsically technical, and its specification is ill-suited for students with modest mathematical sophistication.\nThis difficulty is circumvented by introducing an alternative 'precursor' problem that is easy to understand, and where this understanding can lead to student-devised solutions: how to merge k sorted lists of varying length together as efficiently as possible. Once students have solved this problem, they are better prepared to understand Huffman problem can be trivially reduced to it, and thus and why their merging algorithm solves it. Even the correctness argument is simplified by this approach.

  PublisherOA PDFDOI

• Understanding and misunderstanding the Third International Mathematics and Science Study: what is at stake and why K-12 education studies matter

  Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 · 2009-11-09

  book-chapter1st authorCorresponding

  The technical portion of this paper concerns a videotape classroom study of eighth grade mathematics lessons in Japan, and how methodological design errors led to conclusions that are refuted by the actual video data. We document these errors, and trace their distillation into one- and two-sentence education policy recommendations articulated in U.S. government position papers, implemented in classrooms across the U.S. and imported by countries around the world. We also present the historical context needed to understand the misrepresentations cited in support of questionable education policy.

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• Remarks On Sorting And Parallel Processing

  2005-08-24

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• On Universal Classes of Extremely Random Constant-Time Hash Functions

  SIAM Journal on Computing · 2004-01-01 · 116 citations

  article1st authorCorresponding

  A family of functions F that map [0,m-1] into [0,n-1] is said to be $\h$-wise independent if any tuple of $\h$ distinct points in $[0,m-1]$ have a corresponding image, for a randomly selected $f\in F$, that is uniformly distributed in $[0,n-1]^{\h}$. This paper shows that for suitably fixed $\epsilon < 1$ and any $\h < m^\epsilon$, there are families of $\h$-wise independent functions that can be evaluated in constant time for the standard random access model of computation. It is also proven that any such family requires a storage array of $m^\delta$ random seeds for a suitable $\delta<1$. These seeds can be pseudorandom values precomputed from an initial $O(\h)$ random seeds. A simple adaptation yields $n^\epsilon$-wise independent functions that require $n^\delta$ storage in many cases where $m\gg n$. Lower bounds are presented to show that neither storage requirement can be materially reduced. Previous constructions of random functions having constant evaluation time and sublinear storage exhibited only a constant degree of independence. Unfortunately, the explicit randomized constructions, while requiring a constant number of operations, are far too slow for any practical application. However, nonconstructive existence arguments are given, which suggest that this factor might be eliminated. The problem of eliminating this factor is shown to be equivalent to a fundamental open question in graph theory. As a consequence of these constructions, many probabilistic algorithms---from traditional hashing to Ranade's emulation of common PRAM algorithms---can for the first time be shown to achieve, up to constant factors, their expected asymptotic performance for a programmable, albeit formal and currently impractical, model of computation, and a research direction is now available that may eventually lead to implementations that are fast and provably sound.

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• An Isoperimetric Theorem in Plane Geometry

  Discrete & Computational Geometry · 2003-01-22 · 10 citations

  articleOpen access1st authorCorresponding
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• Median Bounds and Their Application

  Journal of Algorithms · 2001-01-01 · 23 citations

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• Some Dido-type Inequalities

  Elemente der Mathematik · 2001-02-01 · 3 citations

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  Alan Siegel is the product of the Palo Alto public school system in California. He earned his B.S. in mathematics and his Ph.D. in computer science at Stanford University. He is presently the Deputy Chairman for the Department of Computer Science at New York University. His areas of specialty include the mathematical analysis of algorithms, probabilistic analysis, and lower bounds. He is also a cofounder of a project that seeks to improve mathematics education in the U.S.

  PublisherOA PDFDOI

Frequent coauthors

• Jeanette P. Schmidt

  Johannes Gutenberg University Mainz

  19 shared

• Amos Fiat

  8 shared

• Moni Naor

  7 shared

• Richard Cole

  Courant Institute of Mathematical Sciences

  7 shared

• Aravind Srinivasan

  3 shared

• Danny Dolev

  3 shared

• Kenneth M. Morris

  2 shared

• Alexandro Schäffer

  Stanford University

  2 shared