Computer-Aided complexity classification of combinational problems

Authors:
B. J. Lageweg;J. K. Lenstra;E. L. Lawler;A. H. G. Rinnooy Kan
Affiliations:
Mathematisch Centrum, Amsterdam;Mathematisch Centrum, Amsterdam;Univ. of California, Berkeley;Erasmus Univ. Rotterdam, The Netherlands
Venue:
Communications of the ACM
Year:
1982

Citing 3
Cited 7

`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications

Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling Dependent Tasks with Different Arrival Times to Meet Deadlines

Proceedings of the International Workshop organized by the Commision of the European Communities on Modelling and Performance Evaluation of Computer Systems

Proof of the 4/3 conjecture for preemptive vs. nonpreemptive two-processor scheduling

STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Machine learning by schedule decomposition: prospects for an integration of AI and OR techniques for job shop scheduling

Advances in evolutionary computing
Machine scheduling with earliness, tardiness and non-execution penalties

Computers and Operations Research
Heuristics for minimizing maximum lateness on a single machine with family-dependent set-up times

Computers and Operations Research
Minimizing Average Flow Time in Sensor Data Gathering

Algorithmic Aspects of Wireless Sensor Networks
An approximation algorithm for the minimum latency set cover problem

ESA'05 Proceedings of the 13th annual European conference on Algorithms
New directions in scheduling theory

Operations Research Letters

Quantified Score

Hi-index	48.22

Visualization

Abstract

We describe a computer program that has been used to maintain a record of the known complexity results for a class of 4536 machine scheduling problems. The input of the program consists of a listing of known “easy” problems and a listing of known “hard” problems. The program employs the structure of the problem class to determine the implications of these results. The output provides a listing of essential results in the form of maximal easy and minimal hard problems as well as listings of minimal and maximal open problems, which are helpful in indicating the direction of future research. The application of the program to a restricted class of 120 single-machine problems is demonstrated. Possible refinements and extensions to other research areas are suggested. It is also shown that the problem of determining the minimum number of results needed to resolve the status of all remaining open problems in a complexity classification such as ours is itself a hard problem.