Computational Biology
Scribe Notes for Class 10
June 5, 2000
Scribe: J. Zwolak
Today's Handouts and Announcements
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Talk to Dr. Heath this week (if you have not already) about presenting a
topic. Plan on taking 1-2 class periods.
Today's Topics
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The main topic of the day was using the consecutive 1's property to order
probes. Some properties of the problem:
- Sometimes many solutions.
- Always an even number of solutions (every solution has its mirror image).
- If there is no solution then there is an error in the data.
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Fulkerson and Gross -- An algorithm to find the order of
the probes that yields consecutive 1's in each row of the matrix. The naive
approach to this problem yields time complexity O(nm^2). Where n is the number
of probes (columns of the matrix) and m is the number of fragments (rows of the
matrix).
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Booth and Lueker -- Another algorithm to find the order
of the probes. This algorithm uses PQ trees. There is a fast way (O(n)) to combine PQ trees (which seems to be the dominant operation with this algorithm). The time complexity of this algorithm is O(mn).
NOTE: Neither of the algorithms mentioned are specific to ordering probes given
information about which fragments the probes hybridize to. Rather the
algorithms find permutations of the columns of a matrix that yield consecutive
1's in each row.
Today's Sources
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Setubal and Meidanis:
Chapter 5.
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Salzberg, Searls, and Kasif:
None
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Reference [27] from SM. K. S. Booth and G. S. Lueker. Testing of the consecutive ones
property, interval graphs, and graph planarity using PQ-tree algorithms.
Journal of Computer and System Sciences, 13(3):335-379, 1976
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CS6104 Account (cs6104@courses.cs.vt.edu)