Reducing a Target Interval to a Few Exact Queries
- Cite this paper as:
- Nederlof J., van Leeuwen E.J., van der Zwaan R. (2012) Reducing a Target Interval to a Few Exact Queries. In: Rovan B., Sassone V., Widmayer P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg
In exact exponential algorithms, we present new insight into whether Subset Sum and Knapsack have efficient algorithms in both time and space. In particular, we show that the time and space complexity of Subset Sum and Knapsack are equivalent up to a small polynomial factor in the input size. We also give an algorithm that solves sparse instances of Knapsack efficiently in terms of space and time.
In parameterized complexity, we present the first kernelization results on weighted variants of several well-known problems. In particular, we show that weighted variants of Vertex Cover and Dominating Set, Traveling Salesman, and Knapsack all admit polynomial randomized Turing kernels when parameterized by |U|.
Curiously, our method relies on a technique more commonly found in approximation algorithms.
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