Name
Abstract | ||
|---|---|---|
We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length. The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/978-3-642-31113-0_8 | MPC |
Keywords | Field | DocType |
capture dominance,fixed-point calculus,iterative graph algorithm,bridge common practice,shortest path,common practice,dominance algorithm,finite path,graph algorithm,fixed-point fusion,polynomial-time graph algorithm,shortest path algorithm,dominance | Discrete mathematics,Path (graph theory),Line graph,Graph property,Computer science,Directed graph,Theoretical computer science,Null graph,Voltage graph,Graph (abstract data type),Widest path problem | Conference |
Citations | PageRank | References |
4 | 0.41 | 24 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ilya Sergey | 1 | 162 | 16.06 |
| Jan Midtgaard | 2 | 206 | 11.48 |
| Dave Clarke | 3 | 416 | 26.19 |