Md. Shafiul Alam

Three Paths to Point Placement

The point placement problem is to determine the positions of a set of n distinct points, P = {p 1, p 2, p 3, …, p n }, on a line uniquely, up to translation and reflection, from the fewest possible distance queries between pairs of points. Each distance query corresponds to an edge in a graph, called point placement graph (ppg), whose vertex set is P. The uniqueness requirement of the placement translates to line rigidity of the ppg. In this paper, we show how to construct in 2 rounds a line rigid ppg of size 9n/7 + O(1). This improves the best known result of 4n/3 + O(1). We also improve the lower bound on 2-round algorithms from 14n/13 to 9n/8.

More on Generalized Jewels and the Point Placement Problem

The point placement problem is to determine the positions of a set of n distinct points, P = {p1, p2, p3, . . . , pn}, on a line uniquely, up to translation and reflection, from the fewest possible distance queries between pairs of points. Each distance query corresponds to an edge in a graph, called point placement graph (ppg), whose vertex set is P . The uniqueness requirement of the placement translates to line-rigidity of the ppg. In this paper we show how to construct in 2 rounds a line-rigid point placement graph of size 4n/3 + O(1) from certain small-sized graphs called 6:6 jewels. This improves an earlier result that used cycle-graphs on 5 vertices. More significantly, we improve the lower bound on 2-round algorithms from 17n/16 to 12n/11. Submitted: July 2012 Reviewed: February 2013 Revised: May 2013 Accepted: January 2014 Final: February 2014 Published: February 2014 Article type: Regular paper Communicated by: X. He Some parts of this paper appeared in CCCG 2009 [2] and CCCG 2010 [1]. This research was supported by an NSERC discovery grant awarded to the second author. E-mail addresses: alam9@uwindsor.ca (Md. Shafiul Alam ) asishm@uwindsor.ca (Asish Mukhopadhyay) 134 M. S. Alam & A.Mukhopadhyay Point Placement Problem

An Incremental Linear Programming Based Tool for Analyzing Gene Expression Data

The availability of large volumes of gene expression data from microarray analysis (cDNA and oligonucleotide) has opened a new door to the diagnoses and treatments of various diseases based on gene expression profiling. In this paper, we discuss a new profiling tool based on linear programming. Given gene expression data from two subclasses of the same disease (e.g. leukemia), we are able to determine efficiently if the samples are linearly separable with respect to triplets of genes. This was left as an open problem in an earlier study that considered only pairs of genes as linear separators. Our tool comes in two versions - offline and incremental. Tests show that the incremental version is markedly more efficient than the offline one. This paper also introduces a gene selection strategy that exploits the class distinction property of a gene by separability test by pairs and triplets. We applied our gene selection strategy to 4 publicly available gene-expression data sets. Our experiments show that gene spaces generated by our method achieves similar or even better classification accuracy than the gene spaces generated by t-values, FCS(Fisher Criterion Score) and SAM(Significance Analysis of Microarrays).

Algorithms for Problems on Maximum Density Segment

Let A be a sequence of n ordered pairs of real numbers

Control of Constraint Weights for a 2D Autonomous Camera

a_i, l_i

Algorithmic Aspects of Some Problems in Computational Biology

i=1, \ldots , n