APPROXIMATION ALGORITHMS FOR A GRAPH-CUT PROBLEM WITH APPLICATIONS TO A CLUSTERING PROBLEM IN BIOINFORMATICS SALIMUR RASHID CHOUDHURY Bachelor of Science, Islamic University of Technology, 2004 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE Department of Mathematics and Computer Science University of Lethbridge LETHBRIDGE, ALBERTA, CANADA c  Salimur R. Choudhury, 2008