# Complexity and algorithms for reasoning about time: a graph-theoretic approach

@article{Golumbic1993ComplexityAA, title={Complexity and algorithms for reasoning about time: a graph-theoretic approach}, author={Martin Charles Golumbic and Ron Shamir}, journal={J. ACM}, year={1993}, volume={40}, pages={1108-1133} }

Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions, and all realizations problems are considered for temporal (internal) data…

## 242 Citations

### Algorithms and Complexity for Reasoning about Time

- Mathematics, Computer ScienceAAAI
- 1992

This work unifies notions of interval algebras for temporal reasoning in artificial intelligence with those of interval orders and interval graphs in combinatorics, obtaining new algorithmic and complexity results of interest to both disciplines.

### Artin Charles Gchmbic

- Mathematics
- 1999

Interval consistency problems deal with events, each of which is assumed to be an interval on the real line or on any other linearly ordered set. This paper deals with problems in reasoning about…

### Point algebras for temporal reasoning: Algorithms and complexity

- Mathematics, Computer ScienceArtif. Intell.
- 2003

### Trends in Temporal Reasoning: Constraints, Graphs and Posets

- Computer Science, MathematicsMACIS
- 2015

This work reviews temporal reasoning concepts including a method for deciding tractability of temporal constraint satisfaction problems based on the theory of algebraic closure operators for constraints and proposes novel research for scheduling algorithmsbased on the Fishburn-Shepp inequality for posets.

### Temporal Patterns: Smart-type Reasoning and Applications

- Mathematics
- 2017

—Allen’s interval algebra is a calculus for temporal reasoning that was introduced in 1983. Reasoning with qualitative time in Allen’s full interval algebra is nondeterministic polynomial time (NP)…

### Satisfiability Problems on Intervals and Unit Intervals

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1997

### Interval Graphs, Interval Orders and the Consistency of Temporal Events

- MathematicsISTCS
- 1992

This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics.

### Modelling and solving temporal reasoning as propositional satisfiability

- Computer ScienceArtif. Intell.
- 2008

### Coloring Algorithms for Tolerance Graphs: Reasoning and Scheduling with Interval Constraints

- Computer ScienceAISC
- 2002

This paper investigates algorithmic problems on tolerance graphs, a family which generalizes interval graphs, and which therefore have broader application, and presents a coloring algorithm for a tolerance graph on n vertices whose running time is O(n2), given the tolerance representation.

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It is described how representation structures for counting the number of endpoint sequences associated with a given interval order or interval graph can be used in temporal reasoning. Efficient…

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