Romeo Rizzi

Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms

In this paper we address the pure parsimony haplotyping problem: Find a minimum number of haplotypes that explains a given set of genotypes. We prove that the problem is APX-hard and present a 2k- 1-approximation algorithm for the case in which each genotype has at most k ambiguous positions. We further give a new integer-programming formulation that has (for the first time) a polynomial number variables and constraints. Finally, we give approximation algorithms, not based on linear programming, whose running times are almost linear in the input size.

Some simple distributed algorithms for sparse networks

Summary. We give simple, deterministic, distributed algorithms for computing maximal matchings, maximal independent sets and colourings. We show that edge colourings with at most

A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

2\Delta-1

Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications

colours, and maximal matchings can be computed within

The firefighter problem for graphs of maximum degree three

{\cal O}(\log^* n + \Delta)

Polynomial and APX-hard cases of the individual haplotyping problem

deterministic rounds, where

Optimal skewed data allocation on multiple channels with flat broadcast per channel

\Delta

Classes of cycle bases

is the maximum degree of the network. We also show how to find maximal independent sets and

A polynomial case of the parsimony haplotyping problem

(\Delta+1)

Evaluation of BIC-based algorithms for audio segmentation

-vertex colourings within