Parameterized top-K algorithms

  • Authors:

  • Jianer Chen;Iyad A. Kanj;Jie Meng;Ge Xia;Fenghui Zhang

  • Affiliations:

  • Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, USA;School of Computing, DePaul University, 243 S. Wabash Avenue, Chicago, IL 60604, USA;Samsung R&D Center, San Jose, CA 95134, USA;Department of Computer Science, Lafayette College, Easton, PA 18042, USA;Google Kirkland, 747 6th Street South, Kirkland, WA 98033, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

We study algorithmic techniques that produce the best K solutions to an instance of a parameterized NP-hard problem whose solutions are associated with a scoring function. Our parameterized top-K algorithms proceed in two stages. The first stage is a structure algorithm that on a problem instance constructs a structure of feasible size, and the second stage is an enumerating algorithm that produces the K best solutions to the instance based on the structure. We show that many algorithm-design techniques for parameterized algorithms, such as branch-and-search, color coding, and bounded treewidth, can be adopted for designing efficient structure algorithms. We then develop new techniques that support efficient enumerating algorithms. In particular, we show that for a large class of well-known NP optimization problems, there are parameterized top-K algorithms that produce the best K solutions for the problems in feasible amount of average time per solution when the parameter value is small. Finally, we investigate the relation between fixed-parameter tractability and parameterized top-K algorithms.