• Corpus ID: 14173955

Dynamic Graph Algorithms for Connectivity Problems

@inproceedings{cki2015DynamicGA,
  title={Dynamic Graph Algorithms for Connectivity Problems},
  author={Jakub Łącki},
  year={2015}
}
  • J. Łącki
  • Published 26 January 2015
  • Computer Science, Mathematics
In this thesis we present several new algorithms for dynamic graph problems. The common theme of the problems we consider is connectivity. In particular, we study the maintenance of connected components in a dynamic graph, and the Steiner tree problem over a dynamic set of terminals. First, we present an algorithm for decremental connectivity in planar graphs. It processes any sequence of edge deletions intermixed with a set of connectivity queries. Each connectivity query asks whether two… 

References

SHOWING 1-10 OF 56 REFERENCES

A faster approximation algorithm for the Steiner problem in graphs

TLDR
The essence of the algorithm is to find a generalized minimum spanning tree of a graph in one coherent phase as opposed to the previous multiple steps approach.

Dynamic Steiner Tree and Subgraph TSP

TLDR
The Steiner tree problem is studied over a dynamic set of terminals, and appropriate methods that contribute to both online approximation algorithms and dynamic algorithms are developed.

Dynamic Steiner Tree Problem

TLDR
This paper proposes a new problem called the dynamic Steiner tree problem, and it is shown that the worst-case performance for any algorithm is at least $\frac{1}{2}\lg n$ times the cost of an optimum solution with complete rearrangement.

Optimal Decremental Connectivity in Planar Graphs

TLDR
An algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions is shown, which improves over a previously known O(n log n) time algorithm.

Online Steiner Tree with Deletions

TLDR
An online algorithm is given that maintains a Steiner tree under only deletions, and an algorithm that changes only a constant number of edges upon each request, and maintains a constant-competitive tree at all times is given.

Dynamic graph connectivity in polylogarithmic worst case time

TLDR
The technique can be used to simplify and significantly speed up the preprocessing time for the emergency planning problem while matching previous bounds for an update, and to approximate the sizes of cutsets of dynamic graphs in time O(min{|S|, |V\S|}) for an oblivious adversary.

Offline Algorithms for Dynamic Minimum Spanning Tree Problems

TLDR
An efficient algorithm for maintaining a minimum spanning tree (MST) in a graph subject to a sequence of edge weight modifications is described, which performs O(log n) work per modification, where n is the number of vertices in the graph.

An improved LP-based approximation for steiner tree

TLDR
This paper improves the approximation factor for Steiner tree, developing an LP-based approximation algorithm based on a, seemingly novel, iterative randomized rounding technique and shows that the integrality gap of the LP is at most $1.55, hence answering to the mentioned open question.

Separator Based Sparsification. I. Planary Testing and Minimum Spanning Trees

TLDR
A fully dynamic planarity testing algorithm is given that maintains a graph subject to edge insertions and deletions and that allows queries that test whether the graph is currently planar, or whether a potential new edge would violate planarity, inO(n1/2) amortized time per update or query.
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