Related papers: Cutting an alignment with Ockham's razor
The sequence reconstruction problem asks for the recovery of a sequence from multiple noisy copies, where each copy may contain up to $r$ errors. In the case of permutations on \(n\) letters under the Hamming metric, this problem is closely…
We study complexity of rearrangement problems in the generalized breakpoint model and settle several open questions. The model was introduced by Tannier et al. (2009) who showed that the median problem is solvable in polynomial time in the…
We present parametric breadth-first search (PBFS), a new algorithm for solving the parametric minimum cut problem in a network with source-sink-monotone capacities. The objective is to find the set of breakpoints, i.e., the points at which…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
Multiple sequence alignment is a basic procedure in molecular biology, and it is often treated as being essentially a solved computational problem. However, this is not so, and here I review the evidence for this claim, and outline the…
Multiple Sequences Alignment (MSA) of biological sequences is a fundamental problem in computational biology due to its critical significance in wide ranging applications including haplotype reconstruction, sequence homology, phylogenetic…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
The reconstruction of phylogenetic trees from mixed populations has become important in the study of cancer evolution, as sequencing is often performed on bulk tumor tissue containing mixed populations of cells. Recent work has shown how to…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint…
The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every…
Recently, Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer…