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- W2570709797 abstract "Given a graph G = (V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V ×V )E such that the graph H = (V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research [11]. First announced by Kaplan, Tarjan and Shamir in FOCS '94, this problem is known to be FPT [11], but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with O(k5) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem admits a kernel with O(k2) vertices, completing a previous result of Guo [10]." @default.
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- W2570709797 date "2011-01-01" @default.
- W2570709797 modified "2023-09-23" @default.
- W2570709797 title "Polynomial Kernels for Proper Interval Completion and Related Problems" @default.
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- W2570709797 doi "https://doi.org/10.1007/978-3-642-22953-4_20" @default.
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