Pareto Complexity of Two-Parameter FPT Problems: A Case Study for Partial Vertex Cover

We describe a framework for expressing the complexity of algorithms for FPT problems with two separate parameters k, m and with exponential time bounds O∗ (xk ym ) where x, y > 1 are constant bases. An optimal combination of bases x, y can be chosen depending on the ratio m/k. We demonstrate the framework on a graph problem: finding a vertex cover of size k that leaves at most m edges uncovered. We state the best branching rules we could find so far, for all ranges of m/k. Special attention is paid to the extremal cases where either m/k or k/m are close to 0.

• Type: Conference
• Year: 2009
• Where: IWPEC
• Authors: Peter Damaschke
• Keywords: Applied Computing, Exponential Time Bounds, IWPEC 2009, Ratio M/k, Xk Ym