# DIMACS Seminar on Math and CS in Biology

## Title:

On the Complexity and Approximation of Syntenic Distance

## Speaker:

- Bhaskar DasGupta
- Rutgers University, Camden

## Place:

- Seminar Room 431, CoRE Building
- Rutgers University.

## Time:

- 2:00 p.m.
- Thursday, November 7, 1996

Abstract:
(Joint work with T. Jiang, M. Li, S. Kannan and Z. Sweedyk.)

The paper studies the computational complexity and approximation
algorithms for a new evolutionary distance between multi-chromosomal
genomes introduced recently by Ferretti, Nadeau and Sankoff. Here, a
chromosome is represented as a set of genes and a genome is a
collections of chromosomes. The syntenic distance between two genomes
is defined as the minimum number of translocations, fusions and
fissions required to transform one genome into the other. We prove
that computing the syntenic distance is NP-hard and give a simple
approximation algorithm with ratio $2$. The question of how to improve
the approximation ratio is also considered, and a tight connection
between finding large ``balanced'' independent sets in bipartite
graphs and such an improvement is shown. For the case when an upper
bound $d$ on the syntenic distance is known, we show that an an
optimal syntenic sequence can be found in $O(n^2\cdot 2^{O(d^2)})$
time. Next, we show that if the set of operations for transforming a
genome is significantly restricted, we can nevertheless find a
solution that performs at most $O( \log d)$ additional moves, where
$d$ is the number of moves performed by the unrestricted optimum.
This result should help in the design of approximation algorithms.
Finally, we investigate the median problem: Given three genomes,
construct a genome minimizing the total syntenic distance to the three
given genomes. The problem has application in the inference of
phylogenies based on the syntenic distance. We prove that the problem
is NP-hard and design an efficient polynomial time approximation
algorithm with ratio $4+\epsilon$ for any constant $\epsilon>0$.

Document last modified on October 30, 1996