Wyniki wyszukiwania - BazTech

1

Catching a Structural Bug with a Flower

Avellaneda F., Morin R.

Fundamenta Informaticae

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2015

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Vol. 140, nr 1

61--87

EN

Checking the structural boundedness and the structural termination of vector addition systems with states boils down to detecting pathological cycles. As opposed to their non-structural variants which require exponential space, these properties need polynomial time only. The algorithm searches for a counter-example in the form of a multiset of arcs computed by means of linear programming. Yet the minimal length of a pathological cycle can be exponential in the size of the system which makes it difficult to visualize and to analyze the detected bug in details. We propose to describe pathological cycles in the form of particular cycles called flowers. The latter are made of petals which are iterated circuits connected by simple paths that form a calyx. We present an algorithm that builds in polynomial time a flower from the multiset of arcs that represents a pathological cycle. Interestingly the number of petals within a flower is at most equal to the dimension of vectors which helps to describe in a concise way the underlying bug and to analyse it.

2

Lazy shortest path computation in dynamic graphs

Aioanei D.

Computer Science

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2012

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Vol. 13 (3)

113-137

EN

We address the problem of single-source shortest path computation in digraphs with non-negative edge weights subjected to frequent edge weight decreases such that only some shortest paths are requested in-between updates. We optimise a recent semidynamic algorithm for weight decreases previously reported to be the fastest one in various conditions, resulting in important time savings that we demonstrate for the problem of incremental path map construction in usersteered image segmentation. Moreover, we extend the idea of lazy shortest path computation to digraphs subjected to both edge weight increases and decreases, comparing favourably to the fastest recent state-of-the-art algorithm.

3

Route planning in dynamic graphs with linear changing and preprocessing for speed-up

Szűcs G.

Transport Problems

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2010

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T. 5, z. 2

49-58

EN

The goal of this paper is to work out a concept for route planning in a road network, where the costs of roads are not constant, but changing in a linear way. The solution developed is based on the classical Dijkstra's algorithm, which helps to find the route with minimal cost. The new algorithm takes the varying into account in order to find out the best route. This search refers not only to a moment of the departure but to the whole duration of the travel. A speed-up technique has been developed for preprocessing before run time. This preprocessing phase helps to give back the route with minimal cost for the user quickly in run time query. A numerical example has been presented to show the detailed steps of the algorithm and the speed-up technique.

PL

Celem artykułu jest wypracowanie koncepcji planowania tras (trasowania) w sieci drogowej, w której koszty połączeń nie są stałe, lecz zmieniają się w sposób liniowy. Zastosowane rozwiązanie opiera się na klasycznym algorytmie Dijkstra, który umożliwia znajdowanie tras po koszcie minimalnym. Proponowany algorytm uwzględnia dynamiczną różnorodność tras, w celu generowania najkorzystniejszej trasy. Jej poszukiwanie uwzględnia nie tylko momenty rozpoczęcia podróży, ale także czas trwania całej podróży. Technikę przyspieszania (speed-up) rozwinięto, w celu wstępnego przetwarzania przed fazą wykonania. Faza wstępnego przetwarzania pozwala szybciej pozyskać trasę, po koszcie minimalnym dla użytkownika. W artykule zostały zaprezentowane liczne przykłady, w których przedstawiono kolejne kroki algorytmu i techniki przyspieszania.