arXiv subjects

Mohammad-Hadi Foroughmand-Araabi

Publications and source records attributed to Mohammad-Hadi Foroughmand-Araabi.

3 recordsLinked to original sources

arXiv2023

An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models

The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that maximizes the probability of observing a given set of sequences as leaves. The phylogeography problem extends the ancestral maximum-likelihood problem to incorporate geolocation of leaf and internal nodes. While a constant factor approximation algorithm has been established for the ancestral maximum-likelihood problem concerning two-state sequences, no such algorithm has been devised for any generalized instances of the problem. In this paper, we focus on a generalization of the two-state model, the time reversible Markov evolutionary models for sequences and geolocations. Under this evolutionary model, we present a $2\log_2 k $-approximation algorithm, where $k$ is the number of input samples, addressing both the ancestral maximum-likelihood and phylogeography problems. This is the first approximation algorithm for the phylogeography problem. Furthermore, we show how to apply the algorithm on popular evolutionary models like generalized time-reversible (GTR) model and its specialization Jukes and Cantor 69 (JC69).

cs.DS↗

arXiv2021

Mean Isoperimetry with Control on Outliers: Exact and Approximation Algorithms

Given a weighted graph $G=(V,E)$ with weight functions $c:E\to \mathbb{R}_+$ and $π:V\to \mathbb{R}_+$, and a subset $U\subseteq V$, the normalized cut value for $U$ is defined as the sum of the weights of edges exiting $U$ divided by the weight of vertices in $U$. The {\it mean isoperimetry problem}, $\mathsf{ISO}^1(G,k)$, for a weighted graph $G$ is a generalization of the classical uniform sparsest cut problem in which, given a parameter $k$, the objective is to find $k$ disjoint nonempty subsets of $V$ minimizing the average normalized cut value of the parts. The robust version of the problem seeks an optimizer where the number of vertices that fall out of the subpartition is bounded by some given integer $0 \leq ρ\leq |V|$. Our main result states that $\mathsf{ISO}^1(G,k)$, as well as its robust version, $\mathsf{CRISO}^1(G,k,ρ)$, subjected to the condition that each part of the subpartition induces a connected subgraph, are solvable in time $O(k^2 ρ^2\ π(V(T)^3)$ on any weighted tree $T$, in which $π(V(T))$ is the sum of the vertex-weights. This result implies that $\mathsf{ISO}^1(G,k)$ is strongly polynomial-time solvable on weighted trees when the vertex-weights are polynomially bounded and may be compared to the fact that the problem is NP-Hard for weighted trees in general. Also, using this, we show that both mentioned problems, $\mathsf{ISO}^1(G,k)$ and $\mathsf{CRISO}^1(G,k,ρ)$ as well as the ordinary robust mean isoperimetry problem $\mathsf{RISO}^1(G,k,ρ)$, admit polynomial-time $O(\log^{1.5}|V| \log\log |V|)$-approximation algorithms for weighted graphs with polynomially bounded weights, using the R{ä}cke-Shah tree cut sparsifier.

cs.DS↗

arXiv2019

Abstract Geometrical Computation 10: An Intrinsically Universal Family of Signal Machines

Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed in continuous time and space. When signals meet, they get replaced by other signals. A signal machine defines the types of available signals, their speeds and the rules for replacement in collision. A signal machine A simulates another one B if all the space-time diagrams of B can be generated from space-time diagrams of A by removing some signals and renaming other signals according to local information. Given any finite set of speeds S, we construct a signal machine that is able to simulate any signal machine whose speeds belong to S. Each signal is simulated by a macro-signal, a ray of parallel signals. Each macro-signal has a main signal located exactly where the simulated signal would be, as well as auxiliary signals which encode its id and the collision rules of the simulated machine. The simulation of a collision, a macro-collision, consists of two phases. In the first phase, macro-signals are shrunk, then the macro-signals involved in the collision are identified and it is ensured that no other macro-signal comes too close. If some do, the process is aborted and the macro-signals are shrunk, so that the correct macro-collision will eventually be restarted and successfully initiated. Otherwise, the second phase starts: the appropriate collision rule is found and new macro-signals are generated accordingly. Considering all finite set of speeds S and their corresponding simulators provides an intrinsically universal family of signal machines.

cs.FL↗