Partition on trees with supply and demand: Kernelization and algorithms

Mugang Lin, Qilong Feng, Jianer Chen, Wenjun Li

Abstract: Network reconfiguration is an important research topic in the planning and operation of power distribution networks. In this paper, we study the partition problem on trees with supply and demand from parameterized computation perspective. We analyze the relationship between supply nodes and demand nodes, and give four reduction rules, which result in a kernel of size O(k2)<math><mi is="true">O</mi><mo stretchy="false" is="true">(</mo><msup is="true"><mrow is="true"><mi is="true">k</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msup><mo stretchy="false" is="true">)</mo></math> for the problem. Based on branching technique, a parameterized algorithm of running time ⁎O⁎(2.828k)<math><msup is="true"><mrow is="true"><mi is="true">O</mi></mrow><mrow is="true"><mo is="true">⁎</mo></mrow></msup><mo stretchy="false" is="true">(</mo><msup is="true"><mrow is="true"><mn is="true">2.828</mn></mrow><mrow is="true"><mi is="true">k</mi></mrow></msup><mo stretchy="false" is="true">)</mo></math> is presented.