A Dynamic Implicit Adjacency Labelling Scheme for Line Graphs

Morgan, David

doi:10.1007/11534273_26

Cited by 3 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that having an orientation of a graph G one gets a labeling scheme for G in which the label of a vertex v is the number of v together with the numbers of endvertices of the edges leaving v. It follows that the performance bounds from both the paper of Brodal and Fagerberg and the present paper may be reformulated as the relevant space and time bounds for dynamic labeling scheme in graphs of bounded arboricity. The problem of maintaining dynamic adjacency labels was also considered recently by Morgan [12], who focused on the case of line graphs.…”

Section: Introductionmentioning

confidence: 99%

Adjacency queries in dynamic sparse graphs

Kowalik

2007

Information Processing Letters

View full text Add to dashboard Cite

We deal with the problem of maintaining a dynamic graph so that queries of the form "is there an edge between u and v?" are processed fast. We consider graphs of bounded arboricity, i.e., graphs with no dense subgraphs, like for example planar graphs. Brodal and Fagerberg [WADS'99] described a very simple linear-size data structure which processes queries in constant worst-case time and performs insertions and deletions in O(1) and O(log n) amortized time, respectively. We show a complementary result that their data structure can be used to get O(log n) worst-case time for query, O(1) amortized time for insertions and O(1) worst-case time for deletions. Moreover, our analysis shows that by combining the data structure of Brodal and Fagerberg with efficient dictionaries one gets O(log log log n) worst-case time bound for queries and deletions and O(log log log n) amortized time for insertions, with size of the data structure still linear. This last result holds even for graphs of arboricity bounded by O(log k n), for some constant k.

show abstract

Section: Introductionmentioning

confidence: 99%