Edward Reingold | Illinois Institute of Technology (original) (raw)

Papers by Edward Reingold

Information Processing Letters, Dec 30, 1991

Information Processing Letters 40 (1991) 323328 NorthHolland Scheduling on a hypercube Xiaojun Sh... more Information Processing Letters 40 (1991) 323328 NorthHolland Scheduling on a hypercube Xiaojun Shen 30 December 1991 Computer Science Telecommunications Program, University of Missouri Kansas City, 5100 Rockhill Road, Kansas City, MO 64110, USA Edward 1VI. ...

Siam Journal on Discrete Mathematics, Aug 1, 1995

ABSTRACT Bounds are obtained for the solution to the divide-and-conquer recurrence \[M(n) = \max_... more ABSTRACT Bounds are obtained for the solution to the divide-and-conquer recurrence \[M(n) = \max_{k_1 + \cdots + k_p = n} (M(k_1) + M(k_2) +\cdots + M(k_p) + \min (f(k_1), \cdots, f(k_p))),\] for nondecreasing functions fff. Similar bounds are found for the recurrence with "min" replaced by "sum-of-all-but-the-max." Such recurrences appear in the analysis of various algorithms. The bounds follow from analyses of partition trees.

Siam Journal on Computing, 1996

ABSTRACT It is shown that when a graph is represented as a binary connection matrix, the problems... more ABSTRACT It is shown that when a graph is represented as a binary connection matrix, the problems of finding the shortest path between two nodes of a graph, of determining whether the graph has a cycle, and of determining if a graph is strongly connected each require at leastO(n2) operations. Thus the presently known best algorithms are optimal to within a multiplicative constant.

Information Processing Letters, Apr 8, 1994

We show how to maintain efficiently a collection of k dynamic tables in a sequential segment of m... more We show how to maintain efficiently a collection of k dynamic tables in a sequential segment of memory so that the amortized cost of an insertion or deletion is O(k). As a corollary, this provides a simple method of maintaining a set of paired stacks.

International Journal of Applied Mathematics and Computer Science, Dec 1, 2006

In the system level, adaptive fault diagnosis problem we must determine which components (chips) ... more In the system level, adaptive fault diagnosis problem we must determine which components (chips) in a system are defective, assuming the majority of them are good. Chips are tested as follows: Take two chips, say x and y, and have x report whether y is good or bad. If x is good, the answer is correct, but if x is bad, the answer is unreliable and can be either wrong with probability α or right with probability 1 − α. The key to identifying all defective chips is to identify a single good chip which can then be used to diagnose the other chips; the chip problem is to identify a single good chip. In [1] we have shown that the chip problem is closely related to a modified majority problem in the worst case and have used this fact to obtain upper and lower bounds on algorithms for the chip problem. In this paper, we show the limits of this relationship by showing that algorithms for the chip problem can violate lower bounds on average performance for the modified majority problem and we give an algorithm for the "biased chip" problem (a chip is bad with probability p) whose average performance is better than the average cost of the best algorithm for the biased majority problem.

ACM SIGCUE Outlook, 1974

ABSTRACT In response to a large (currently 2000 students per semester) and increasing enrollment ... more ABSTRACT In response to a large (currently 2000 students per semester) and increasing enrollment in introductory computer science courses, we have started a project to automate these courses on the PLATO IV Computer-Based Education system at the University of Illinois. The key components of our automated course are: 1. a library of lessons, covering several programming languages, computing techniques, and application areas 2. a completely self-contained interactive programming system for the preparation, execution and debugging of programs written by students in any of the languages covered by the lessons 3. a conversational advice-giving and information retrieval system to guide the student through the library of lessons, based on his goals and past performance. The goals and current status of this project are described.

IEEE Transactions on Software Engineering, 1981

We provide a set of "natural" requirements for well-orderings of(binary) list structure... more We provide a set of "natural" requirements for well-orderings of(binary) list structures. We show that the resultant order-type is thesuccessor of the first critical epsilon number.The checker has to verify that the process comes to an end. Hereagain he should be assisted by the programmer giving a furtherdefinite assertion to be verified. This may take the form of a quantitywhich is asserted to decrease continually and vanish when themachine stops. To the pure mathematician it is...

Mathematical Systems Theory, 1972

Software: Practice and Experience, 1990

A unified, algorithmic presentation is given for the Gregorian (current civil), ISO, Julian (old ... more A unified, algorithmic presentation is given for the Gregorian (current civil), ISO, Julian (old civil), Islamic (Moslem), and Hebrew (Jewish) calendars. Easy conversion among these calendars is a byproduct of the approach, as is the determination of secular and religious holidays.

Software: Practice and Experience, 1991

We present a modification of the spring-embedder model of Eades [Congressus Numerantiurn, 42, 149... more We present a modification of the spring-embedder model of Eades [Congressus Numerantiurn, 42, 149-160, (1984)) for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm.

Software: Practice and Experience, 1993

Algorithmic presentations are given for three calendars of historical interest, the Mayan, French... more Algorithmic presentations are given for three calendars of historical interest, the Mayan, French Revolutionary, and Old Hindu.

SIAM Journal on Discrete Mathematics, 1995

SIAM Journal on Computing, 1993

ABSTRACT A function is unimodal if it strictly increases to a unique maximum and then strictly de... more ABSTRACT A function is unimodal if it strictly increases to a unique maximum and then strictly decreases. The problem of determining the smallest possible interval containing the maximum of a unimodal function, by probing only at integer values is studied. In the finite case, the search takes place over the range 0 to N, while in the infinite case the search takes place over the nonnegative integers. The analyses are based on an unusual Fibonacci version of Kraft’s inequality.

SIAM Journal on Computing, 1997

ABSTRACT Given a set of n elements each of which is either red or blue, it is known that in the w... more ABSTRACT Given a set of n elements each of which is either red or blue, it is known that in the worst case n-ν(n) pairwise equal/not equal color comparisons are necessary and sufficient to determine the majority color, where ν(n) is the number of 1-bits in the binary representation of n. We prove that 2n 3-8n 9π+O(logn) such comparisons are necessary and sufficient in the average case.

SIAM Journal on Computing, 1991

ABSTRACT Given a function F: N + →(X,Y} with the property that if F(n 0 )=Y then F(n)=Y for all n... more ABSTRACT Given a function F: N + →(X,Y} with the property that if F(n 0 )=Y then F(n)=Y for all n>n 0 , the unbounded search problem is to use tests of the form “is F(i)=X? '' to determine the smallest n such that F(n)=Y; the “cost” of a search algorithm is a function c(n), the number of such tests used when the location of the first Y is n. A solution to this search problem specifies a prefix-free, binary encoding of the positive integers in which the cost c(n) is the number of bits used to encode n. It is shown that the “ultimate algorithm”, of J. L. Bentley and A. Yao [Inform. Processing Letters 5, 82-87 (1976; Zbl 0335.68030)], which is within an additive Θ(lg * n) factor of a lower bound on the cost of this problem, is “far” from optimal in the sense that it is just the second in an infinite sequence of search algorithms, each of which is much closer to optimality than its predecessor. A corresponding sequence of lower bounds is also given, based on Kraft’s inequality, each of which is much stronger than its predecessor. Diagonalizing over this sequence of search algorithms yields an algorithm, which is given explicitly in a Pascal-like notation, that is within an additive factor of α(n)+2 of the corresponding lower bound, where α (n) is a functional inverse of Ackermann’s function - an extremely slowly growing function. For each search algorithm, the corresponding prefix-free, binary encoding of the integers is given, together with the decoding algorithm. Finally, algorithms/encodings are constructed that differ from the lower bounds by only negligible amounts even for the asymmetric case in which the cost of a Y answer and the cost of an X answer are not the same. In Part II [reviewed below; (Zbl 0716.68047)] it is shown how to continue the construction to get a transfinite sequence of dramatically better algorithms/encodings and lower bounds.