Fast Dynamic Graph Algorithms for Parameterized Problems

  • Yoichi Iwata
  • Keigo Oka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)


Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are o(|G|), that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT).

We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion parameterized by the solution size k. These dynamic graphs achieve almost the best possible update time O(poly(k)logn) and the query time O(f(poly(k),k)), where f(n,k) is the time complexity of any static graph algorithm for the problems. We obtain these results by dynamically maintaining an approximate solution which can be used to construct a small problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm for Cluster Vertex Deletion. Until now, only quadratic time kernelization algorithms are known for this problem.


Time Complexity Vertex Cover Query Time Static Algorithm Cluster Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yoichi Iwata
    • 1
  • Keigo Oka
    • 1
  1. 1.Department of Computer Science Graduate School of Information Science and TechnologyThe University of TokyoJapan

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