David Fernández-Baca

Allocating modules to processors in a distributed system

The author studies the complexity of the problem of allocating modules to processes in a distributed system to minimize total communication and execution costs. He shows that unless P=NP, there can be no polynomial-time epsilon -approximate algorithm for the problem, nor can there exist a local search algorithm that requires polynomial time per iteration and yields an optimum assignment. Both results hold even if the communication graph is planar and bipartite. On the positive side, it is shown that if the communication graph is a partial k-tree or an almost-tree with parameter k, the module allocation problem can be solved in polynomial time. >

A Polynomial-Time Algorithm for the Perfect Phylogeny Problem when the Number of Character States is Fixed

This paper presents a polynomial-time algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of possible states for a character is fixed. This solves a longstanding open problem. This result should be contrasted with the proof by Steel [J. Classification, 9(1992), pp. 91--116] and Bodlaender, Fellows, and Warnow [Proceedings of the19th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science, 1992, pp. 273--283] that the perfect phylogeny problem is NP complete in general.

Robinson-Foulds Supertrees

BackgroundSupertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.ResultsWe introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (naïve) solutions by a factor of Θ(n) and Θ(n2) respectively (where n is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.ConclusionsOur heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.

Performance of Flip Supertree Construction with a Heuristic Algorithm

Supertree methods are used to assemble separate phylogenetic trees with shared taxa into larger trees (supertrees) in an effort to construct more comprehensive phylogenetic hypotheses. In spite of much recent interest in supertrees, there are still few methods for supertree construction. The flip supertree problem is an error correction approach that seeks to find a minimum number of changes (flips) to the matrix representation of the set of input trees to resolve their incompatibilities. A previous flip supertree algorithm was limited to finding exact solutions and was only feasible for small input trees. We developed a heuristic algorithm for the flip supertree problem suitable for much larger input trees. We used a series of 48- and 96-taxon simulations to compare supertrees constructed with the flip supertree heuristic algorithm with supertrees constructed using other approaches, including MinCut (MC), modified MC (MMC), and matrix representation with parsimony (MRP). Flip supertrees are generally far more accurate than supertrees constructed using MC or MMC algorithms and are at least as accurate as supertrees built with MRP. The flip supertree method is therefore a viable alternative to other supertree methods when the number of taxa is large.

iGTP: A software package for large-scale gene tree parsimony analysis

BackgroundThe ever-increasing wealth of genomic sequence information provides an unprecedented opportunity for large-scale phylogenetic analysis. However, species phylogeny inference is obfuscated by incongruence among gene trees due to evolutionary events such as gene duplication and loss, incomplete lineage sorting (deep coalescence), and horizontal gene transfer. Gene tree parsimony (GTP) addresses this issue by seeking a species tree that requires the minimum number of evolutionary events to reconcile a given set of incongruent gene trees. Despite its promise, the use of gene tree parsimony has been limited by the fact that existing software is either not fast enough to tackle large data sets or is restricted in the range of evolutionary events it can handle.ResultsWe introduce iGTP, a platform-independent software program that implements state-of-the-art algorithms that greatly speed up species tree inference under the duplication, duplication-loss, and deep coalescence reconciliation costs. iGTP significantly extends and improves the functionality and performance of existing gene tree parsimony software and offers advanced features such as building effective initial trees using stepwise leaf addition and the ability to have unrooted gene trees in the input. Moreover, iGTP provides a user-friendly graphical interface with integrated tree visualization software to facilitate analysis of the results.ConclusionsiGTP enables, for the first time, gene tree parsimony analyses of thousands of genes from hundreds of taxa using the duplication, duplication-loss, and deep coalescence reconciliation costs, all from within a convenient graphical user interface.

Fast algorithms for bipartite network flow

We discuss network flow in a bipartite graph G with node sets S and T. We show that Karzanov’s algorithm runs in time

LATIN 2012: Theoretical Informatics

O(|S|^2 |T|)

Improved Heuristics for Minimum-Flip Supertree Construction

on G, and that the MPM algorithm can be modified to run in the same bound. For the common case that the degree of each node in T is bounded by a constant, we show that a modified version of the MPM algorithm runs in time

The Perfect Phylogeny Problem

O(|S|^3 + |S||T|)

Minimum-Flip Supertrees: Complexity and Algorithms

on G. The importance of these results comes from the common occurrence of problems that can be modeled and solved using network flow on bipartite graphs where