B. Moller and M. Russling. Shorter paths to graph algorithms. Science of Computer Programming, 22(1-2), April 1994. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Calculating with Relations for Graph Algorithmics - Ravelo (1997) (Correct)
....operation Same is built on, and corresponds to the use given to, Find . Components Q and Phi calculated above can be defined in terms of, respectively, Same and Union using the extreme vertices of edge e as parameters. 8 5 Conclusions Other calculational treatments of graph algorithms include [2, 7, 11, 13, 14]. In all of them, with the exception of [7] the calculations performed on the algorithmic component of the problems can be discriminated from the calculations on the graphs, which are just data manipulated by the algorithms. In appealing to the separation of concerns principle, one should aim ....
....from the calculations on the graphs, which are just data manipulated by the algorithms. In appealing to the separation of concerns principle, one should aim at making clear at all stages what part of the product under construction is being worked on. Such a separation is not very clear in [11, 13, 14], where the relational frameworks used aid the manipulation of both sides of the coin. In [2] where an algebra of matrices for modelling graphs is combined with conventional techniques of imperative programming, the separation is clear. Gibbons s work [7] is exceptional since it proposes an ....
B. Moller and M. Russling. Shorter paths to graph algorithms. Science of Computer Programming, 22(1-2), April 1994.
An Initial-Algebra Approach to Directed Acyclic Graphs - Gibbons (1995) (4 citations) (Correct)
....declaratively manipulating the resulting depth first search forest. Burton and Yang [8] implement graphs in a pure functional language effectively by implementing an imperative store and threading this through the program. 2 3 Fig. 18. A cyclic graph 6. 3 Formal Languages and Relations Moller [24, 25, 26] uses formal languages, and in particular multiary relations, to model graphs. He derives a number of graph algorithms, such as reachability, topological sort and cycle detection. This approach gives concise specifications and calculations. However, graphs are still modelled monolithically there ....
Bernhard Moller and Martin Russling. Shorter paths to graph algorithms. In Bird et al. [3], pages 250--268.
A Relational Approach To Optimization Problems - Curtis (1996) (6 citations) (Correct)
....for designing hardware, for example see the work of Jones, Sheeran and Hutton [90, 49, 91, 45, 50] ffl Relations have also been used to reason about graphs. Schmidt and Strohleins wrote [86] Relations of arbitrary arity have also been used to represent graphs in the work of Moller and Russling [72, 71, 70, 73, 83, 84]. ffl Bird and Meertens developed a formalism for functional programming [6, 7, 69] The research of Bird and de Moor later focused on optimization problems, which are more simply specified using relations: functions cannot express the non determinism inherent in taking a minimum accurately, as ....
B. Moller and M. Russling. Shorter paths to graph algorithms. Science of Computer Programming, 22:157--180, 1994.
A Class of Graph Algorithms - Ravelo (1996) (Correct)
....(instead of proved correct) functional (instead of imperative) algorithms. Formalisation of the points extension of the calculus was the key to a succesful development. The same class of graph problems has also been tackled by other computer scientists using different calculational frameworks [5, 38, 42]. There are two main features brought together in this work. On one hand, a variety of algorithms linked to the well developed subject of graph theory and, on the other hand, new methodologies for algorithm design characterised by their emphasis on calculation. A brief account of these subjects ....
....concepts along with applications to databases, games and program verification. More concerned with algorithm derivation, Moller has developed a calculus of formal languages and relations with which compact calculations of some graph and pointer algorithms have been successfully carried out [37, 38, 42]. In his framework, relations are only used to reason about data, while algorithms are manipulated at a functional level. Indeterminacy and partiality are dealt with via set valued functions, so a relational treatment of algorithms is present in spirit yet not explicitly. The other important ....
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B. Moller and M. Russling. Shorter paths to graph algorithms. Science of Computer Programming, 22(1-2), April 1994.
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