Theory of linear and integer programming
Theory of linear and integer programming
Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
The shifting bottleneck procedure for job shop scheduling
Management Science
Artificial Intelligence - Special issue on knowledge representation
An introduction to parallel algorithms
An introduction to parallel algorithms
Scheduling real-time computations with separation constraints
Information Processing Letters
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Linear programming
Theoretical Computer Science
Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scaling Algorithms for the Shortest Paths Problem
SIAM Journal on Computing
Issues in temporal reasoning for autonomous control systems
AGENTS '98 Proceedings of the second international conference on Autonomous agents
Bounded Model Checking Using Satisfiability Solving
Formal Methods in System Design
Scheduling Algorithms
Real-Time Database and Information
Real-Time Database and Information
Introduction to Algorithms
Parametric Dispatching of Hard Real-Time Tasks
IEEE Transactions on Computers
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
SAT-Based Procedures for Temporal Reasoning
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
Automatic Verification of Sequential Circuit Designs
CHDL '93 Proceedings of the 11th IFIP WG10.2 International Conference sponsored by IFIP WG10.2 and in cooperation with IEEE COMPSOC on Computer Hardware Description Languages and their Applications
Data-Structures for the Verification of Timed Automata
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
Verifying temporal constraints on data in multi-rate transactions using timed automata
RTCSA '00 Proceedings of the Seventh International Conference on Real-Time Systems and Applications
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
An Analysis of Totally Clairvoyant Scheduling
Journal of Scheduling
A greedy strategy for detecting negative cost cycles in networks
Future Generation Computer Systems - Special issue: High-speed networks and services for data-intensive grids: The DataTAG project
Optimizing over Consecutive 1's and Circular 1's Constraints
SIAM Journal on Optimization
"Ratio Regions": A Technique for Image Segmentation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
Stressing is better than relaxing for negative cost cycle detection in networks
ADHOC-NOW'05 Proceedings of the 4th international conference on Ad-Hoc, Mobile, and Wireless Networks
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Chain Programming is a restricted form of Linear Programming with a number of interesting properties. A Chain Program is characterized by a total ordering on the program variables (of a linear program). In other words, the constraints x1 ≤ x2...xn are either implicitly or explicitly part of the constraint system defined by a linear program. At the present juncture, it is not clear whether an arbitrary linear program augmented with a chain is easier to solve than linear programs in general, either asymptotically or computationally; however, it is definitely the case that Chain Programs possess a number of useful properties. In this paper, we restrict ourselves to linear programs that are constituted entirely of difference constraints. For such linear programs (also called Difference Constraint Systems), we show that the total ordering of the program variables results in an elegant divide and conquer algorithm for the problem of feasibility testing. This approach can be parallelized in straightforward fashion to run on any SIMD or MIMD architecture, thereby greatly enhancing its effectiveness. Inasmuch as difference constraint logic is an integral part of a number of verification problems in both Model-checking and real-time scheduling, our result is of particular importance to these communities. Secondly, difference constraint systems are duals of shortest path problems in directed graphs and hence our study is important from the perspectives of the Artificial Intelligence and Operations Research communities as well. One of the surprising consequences of our research is the establishment of a link between Chain Programs over Difference Constraints (CPD) and a specialized class of Totally Unimodular (TUM) matrices called interval matrices. This connection makes it likely that there exists a more efficient algorithm for the problem of feasibility testing in CPDs.