Abstract
We define and study a combinatorial problem called WEIGHTED DIAGNOSTIC COVER (WDC) that models the use of a laboratory technique called genotyping in the diagnosis of a important class of chromosomal aberrations. An optimal solution to WDC would enable us to define a genetic assay that maximizes the diagnostic power for a specified cost of laboratory work. We develop approximation algorithms for WDC by making use of the well-known problem SET COVER for which the greedy heuristic has been extensively studied. We prove worst-case performance bounds on the greedy heuristic for WDC and for another heuristic we call directional greedy. We implemented both heuristics. We also implemented a local search heuristic that takes the solutions obtained by greedy and dir-greedy and applies swaps until they are locally optimal. We report their performance on a real data set that is representative of the options that a clinical geneticist faces for the real diagnostic problem. Many open problems related to WDC remain, both of theoretical interest and practical importance.
Supported by NSF under grant CCR-9508545 and ARO under grant DAAH 04-961-0013
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Kosaraju, S.R., Schäffer, A.A., Biesecker, L.G. (1997). Approximation algorithms for a genetic diagnostics problem. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_49
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DOI: https://doi.org/10.1007/3-540-63307-3_49
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