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Numbering action vertices in workflow graphs

100%
Mann Z.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 3
591-600
EN
Workflow graphs, consisting of actions, events, and logical switches, are used to model business processes. In order to easily identify the actions within a workflow graph, it is useful to number them in such a way that the numbering reflects the structure of the workflow. However, available tools offer only rudimental numbering schemes. In the paper, a set of natural requirements is defined that a logical numbering should fulfill. It is investigated under what conditions there is an appropriate numbering at all, when it is uniquely defined by the set of requirements, and when it can be computed efficiently. It is shown that for an important special class of workflow graphs, namely, structured workflow graphs, the answer to all these questions is affirmative. For general workflow graphs, a set of requirements is presented that can always be fulfilled, but the numbering is not necessarily unique. An algorithm based on a depth-first search can be used to compute an appropriate numbering efficiently.
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Accelerating backtrack search with a best-first-search strategy

63%
Mann Z., Szép T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
901-916
EN
Backtrack-style exhaustive search algorithms for NP-hard problems tend to have large variance in their runtime. This is because "fortunate" branching decisions can lead to finding a solution quickly, whereas “unfortunate” decisions in another run can lead the algorithm to a region of the search space with no solutions. In the literature, frequent restarting has been suggested as a means to overcome this problem. In this paper, we propose a more sophisticated approach: a best-firstsearch heuristic to quickly move between parts of the search space, always concentrating on the most promising region. We describe how this idea can be efficiently incorporated into a backtrack search algorithm, without sacrificing optimality. Moreover, we demonstrate empirically that, for hard solvable problem instances, the new approach provides significantly higher speed-up than frequent restarting.
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