Minimum Cycle Bases and Their Applications

Berger, Franziska; Gritzmann, Peter; Vries, Sven de

doi:10.1007/978-3-642-02094-0_2

Cited by 5 publications

(3 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned in Section 3, computing a minimum-weight cycle basis is not trivial. Several algorithms have been proposed [10,11].…”

Section: Computing the CCC For Control Flow Graphsmentioning

confidence: 99%

The cross cyclomatic complexity: a bi-dimensional measure for program complexity on graphs

Tremblay¹,

Petrillo²

2020

Preprint

View full text Add to dashboard Cite

Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number of branches in a program, it clearly not sufficient to represent the complexity in a piece of software. In this paper, we introduce the cross cyclomatic complexity (CCC), a new bi-dimensional complexity measure on graphs that combines the cyclomatic complexity and the weight of a minimum-weight cycle basis in as pair on the Cartesian plan to characterize program complexity using control flow graphs. Our postulates open a new venue to represent program complexity, and we discuss its implications and opportunities.Keywords cyclomatic complexity, software metrics, software quality, cycle basis, graph 1 Visser et al. propose good software system should have the majority of its methods with a MCC lower or equal 10. Then, a method with MCC of 100 should be considered as very complex.

show abstract

“…As mentioned in Section 3, computing a minimum-weight cycle basis is not trivial. Several algorithms have been proposed [10,11].…”

Section: Computing the CCC For Control Flow Graphsmentioning

confidence: 99%

The cross cyclomatic complexity: a bi-dimensional measure for program complexity on graphs

Tremblay¹,

Petrillo²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…dominates the other invariant. (Note that, using the weighted representation would result in the ordered weight vectors (6,6,9,9,10) and (6,8,9,9,9) with all corresponding cycles being essential).…”

Section: Cyclic Graph Invariantsmentioning

confidence: 99%

Computing cyclic invariants for molecular graphs

2017

Self Cite

View full text Add to dashboard Cite

Ring structures in molecules belong to the most important substructures for many applications in Computational Chemistry. One typical task is to find an implicit description of the ring structure of a molecule. We present efficient algorithms for cyclic graph invariants that may serve as molecular descriptors to accelerate database searches. Another task is to construct a well‐defined set of rings of a molecular graph explicitly. We give a new algorithm for computing the set of relevant cycles of a graph. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 116–131 2017

show abstract

“…The weight vector of a weighted graph G is a vector containing the weights of cycles of an MCB in order of non-decreasing weight. Finding such a vector has applications in chemistry and biology [3]. From our implicit representation of an MCB, we obtain an O(n 3/2 log n) time and O(n 3/2 ) space algorithm for finding the weight vector of a planar graph.…”

Section: Introductionmentioning

confidence: 99%

Minimum Cycle Basis and All-Pairs Min Cut of a Planar Graph in Subquadratic Time

Wulff-Nilsen

2009

Preprint

View full text Add to dashboard Cite

A minimum cycle basis of a weighted undirected graph G is a basis of the cycle space of G such that the total weight of the cycles in this basis is minimized. If G is a planar graph with non-negative edge weights, such a basis can be found in O(n 2 ) time and space, where n is the size of G. We show that this is optimal if an explicit representation of the basis is required. We then present an O(n 3/2 log n) time and O(n 3/2 ) space algorithm that computes a minimum cycle basis implicitly. From this result, we obtain an output-sensitive algorithm that explicitly computes a minimum cycle basis in O(n 3/2 log n + C) time and O(n 3/2 + C) space, where C is the total size (number of edges and vertices) of the cycles in the basis. These bounds reduce to O(n 3/2 log n) and O(n 3/2 ), respectively, when G is unweighted. We get similar results for the all-pairs min cut problem since it is dual equivalent to the minimum cycle basis problem for planar graphs. We also obtain O(n 3/2 log n) time and O(n 3/2 ) space algorithms for finding, respectively, the weight vector and a Gomory-Hu tree of G. The previous best time and space bound for these two problems was quadratic. From our Gomory-Hu tree algorithm, we obtain the following result: with O(n 3/2 log n) time and O(n 3/2 ) space for preprocessing, the weight of a min cut between any two given vertices of G can be reported in constant time. Previously, such an oracle required quadratic time and space for preprocessing. The oracle can also be extended to report the actual cut in time proportional to its size.

show abstract

Minimum Cycle Bases and Their Applications

Cited by 5 publications

References 33 publications

The cross cyclomatic complexity: a bi-dimensional measure for program complexity on graphs

The cross cyclomatic complexity: a bi-dimensional measure for program complexity on graphs

Computing cyclic invariants for molecular graphs

Minimum Cycle Basis and All-Pairs Min Cut of a Planar Graph in Subquadratic Time

Contact Info

Product

Resources

About