Edward G. Coffman

Bin Packing Approximation Algorithms: Combinatorial Analysis

In the classical version of the bin packing problem one is given a list L = (a 1,...,a n ) of items (or elements) and an infinite supply of bins with capacity C. A function s(a i ) gives the size of item a i , and satisfies 0 < s(a i )≤C, 1 ≤ i ≤ n. The problem is to pack the items into a minimum number of bins under the constraint that the sum of the sizes of the items in each bin is no greater than C. In simpler terms, a set of numbers is to be partitioned into a minimum number of blocks subject to a sum constraint common to each block. We use the bin packing terminology, as it eases considerably the problem of describing and analyzing algorithms.

Random-order bin packing

The average-case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [C. Kenyon, Best-fit bin-packing with random order, in: Proc. of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 1996, pp. 359-364] Kenyon introduced the random-order ratio, a new average-case performance metric for bin packing heuristics, and gave upper and lower bounds for it for the Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst-case, i.e., it is 2.

An efficient algorithm for finding ideal schedules

We study the problem of scheduling unit execution time jobs with release dates and precedence constraints on two identical processors. We say that a schedule is ideal if it minimizes both maximum and total completion time simultaneously. We give an instance of the problem where the min-max completion time is exceeded in every preemptive schedule that minimizes total completion time for that instance, even if the precedence constraints form an intree. This proves that ideal schedules do not exist in general when preemptions are allowed. On the other hand, we prove that, when preemptions are not allowed, then ideal schedules do exist for general precedence constraints, and we provide an algorithm for finding ideal schedules in O(n3) time, where n is the number of jobs. In finding such ideal schedules we resolve a conjecture of Baptiste and Timkovsky (Math. Methods Oper. Res. 60(1):145–153, 2004) Further, our algorithm for finding min-max completion-time schedules requires only O(n3) time, while the most efficient solution to date has required O(n9) time.

Self-Organizing Sleep-Wake Sensor Systems

We propose a self-organizing sleep-wake sensor system that is scalable, easily implemented, and energy conserving. An application of concepts from cellular automata theory accounts for much of its novelty. As a surprising by product of its self-organizing behavior, the system has additional, highly desirable properties such as a self-healing capability, fault tolerance, asynchronous operation, seamless accommodation of obstacles in the sensor field, and effectiveness even in the case of intelligent intruders who know sensor design and sensor locations. System performance is a focus of the paper, along with the inverse problem of cellular automata, and self-organizing systems in general: How does one set local rules and initial states so as to achieve pre-specified behavior? Our experimental studies show that broad classes of behavior can be achieved by design, especially by the placement of artificial nucleation centers.

Synthesis of local-rule processes: successes and challenges (abstract only)

How does one systematically program global computations in systems of a vast number of components restricted to local-rule interaction in a flat hierarchy? This question has been around since the 50s when cellular automata were introduced as models of such systems. The question posed here is known as the synthesis problem, and remains poorly understood. Terms like self-assembling and self-organizing are often used to describe computations on such systems. We mention a number of instances of local-rule processes at widely different scales in computer and network engineering: molecular computation, sensor-network computation, and computation on the Web. Typical performance questions that we address include the convergence to useful, non-degenerate behavior: does it always occur, and if so, how long does it take.

A Computational Study of Margining Portfolios of Options by Two Approaches

This paper presents preliminary results of a computational experiment with the strategy-based approach and the risk-based approach to portfolio margining with the purpose to clarify which one yields lower margin requirements under different scenarios. There exists a widespread opinion that the risk-based approach is always a winner in this competition, and therefore the strategy-based approach must be disqualified as outdated. However, the results of our experiment with portfolios of stock options show that, in many practical situations, the strategy-based approach yields substantially lower margin requirements in comparison with the risk-based approach.