Abstract
The gist of many (NP-)hard combinatorial problems is to decide whether a universe of n elements contains a witness consisting of k elements that match some prescribed pattern. For some of these problems there are known advanced algebra-based FPT algorithms which solve the decision problem but do not return the witness. We investigate techniques for turning such a YES/NO-decision oracle into an algorithm for extracting a single witness, with an objective to obtain practical scalability for large values of n. By relying on techniques from combinatorial group testing, we demonstrate that a witness may be extracted with O(klogn) queries to either a deterministic or a randomized set inclusion oracle with one-sided probability of error. Furthermore, we demonstrate through implementation and experiments that the algebra-based FPT algorithms are practical, in particular in the setting of the k-path problem. Also discussed are engineering issues such as optimizing finite field arithmetic.
P.K. supported by the Academy of Finland, grants 252083 and 256287. Ł.K. supported by National Science Centre of Poland, grant number UMO-2013/09/B/ST6/03136.
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Björklund, A., Kaski, P., Kowalik, Ł. (2014). Fast Witness Extraction Using a Decision Oracle. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_13
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DOI: https://doi.org/10.1007/978-3-662-44777-2_13
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