DIMACS Seminar on Math and CS in Biology


Nonoverlapping Local Alignments (Weighted independent sets of axis-parallel rectangles)


Dr. Vineet Bafna


Room 402, Computer Science Building
35 Olden Street, Princeton University.


3:00 PM
Monday, February 20, 1995


We consider the following problem motivated by an application in computational molecular biology. We are given a set of weighted axis-parallel rectangles such that for any pair and either axis, the projection of one rectangle on the axis does not enclose that of the other. Define a pair to be independent if their projections in both axes are disjoint. The problem is to find a maximum-weight independent subset of rectangles.

We show that the problem is NP-hard even in the uniform case when all the weights are the same. We analyze the performance of a natural local-improvement heuristic for the problem and prove a performance ratio of 3.25. We extend the heuristic to the problem of finding a maximum-weight independent set in $(d+1)$-claw free graphs, and show a tight performance ratio of $d - 1 + \frac{1}{d}$. A performance ratio of $\frac{d}{2}$ was known for the heuristic when applied to the uniform case. Our contributions are proving the hardness of the problem and providing a tight analysis of the local-improvement algorithm for the general weighted case.

This is joint work with Babu Narayanan and R. Ravi.

Future speakers

Feb 27: Dr. Laszlo Szekely

March 6: Dr. Robert Vrijenhoek

Document last modified on February 17, 1995