David G. Harris

A New Method for Estimating Species Age Supports the Coexistence of Malaria Parasites and Their Mammalian Hosts

Species in the genus Plasmodium cause malaria in humans and infect a variety of mammals and other vertebrates. Currently, estimated ages for several mammalian Plasmodium parasites differ by as much as one order of magnitude, an inaccuracy that frustrates reliable estimation of evolutionary rates of disease-related traits. We developed a novel statistical approach to dating the relative age of evolutionary lineages, based on Total Least Squares regression. We validated this lineage dating approach by applying it to the genus Drosophila. Using data from the Drosophila 12 Genomes project, our approach accurately reconstructs the age of well-established Drosophila clades, including the speciation event that led to the subgenera Drosophila and Sophophora, and age of the melanogaster species subgroup. We applied this approach to hundreds of loci from seven mammalian Plasmodium species. We demonstrate the existence of a molecular clock specific to individual Plasmodium proteins, and estimate the relative age of mammalian-infecting Plasmodium. These analyses indicate that: 1) the split between the human parasite Plasmodium vivax and P. knowlesi, from Old World monkeys, occurred 6.1 times earlier than that between P. falciparum and P. reichenowi, parasites of humans and chimpanzees, respectively; and 2) mammalian Plasmodium parasites originated 22 times earlier than the split between P. falciparum and P. reichenowi. Calibrating the absolute divergence times for Plasmodium with eukaryotic substitution rates, we show that the split between P. falciparum and P. reichenowi occurred 3.0–5.5 Ma, and that mammalian Plasmodium parasites originated over 64 Ma. Our results indicate that mammalian-infecting Plasmodium evolved contemporaneously with their hosts, with little evidence for parasite host-switching on an evolutionary scale, and provide a solid timeframe within which to place the evolution of new Plasmodium species.

Constraint satisfaction, packet routing, and the lovasz local lemma

Constraint-satisfaction problems (CSPs) form a basic family of NP-hard optimization problems that includes satisfiability. Motivated by the sufficient condition for the satisfiability of SAT formulae that is offered by the Lovasz Local Lemma, we seek such sufficient conditions for arbitrary CSPs. To this end, we identify a variable-covering radius--type parameter for the infeasible configurations of a given CSP, and also develop an extension of the Lovasz Local Lemma in which many of the events to be avoided have probabilities arbitrarily close to one; these lead to a general sufficient condition for the satisfiability of arbitrary CSPs. One primary application is to packet-routing in the classical Leighton-Maggs-Rao setting, where we introduce several additional ideas in order to prove the existence of near-optimal schedules; further applications in combinatorial optimization are also shown.

Lopsidependency in the Moser-Tardos Framework: Beyond the Lopsided Lovász Local Lemma

The Lopsided Lovász Local Lemma (LLLL) is a powerful probabilistic principle that has been used in a variety of combinatorial constructions. While this principle began as a general statement about probability spaces, it has recently been transformed into a variety of polynomial-time algorithms. The resampling algorithm of Moser and Tardos [2010] is the most well-known example of this. A variety of criteria have been shown for the LLLL; the strongest possible criterion was shown by Shearer, and other criteria that are easier to use computationally have been shown by Bissacot et al. [2011], Pegden [2014], Kolipaka and Szegedy [2011], and Kolipaka et al. [2012]. We show a new criterion for the Moser-Tardos algorithm to converge. This criterion is stronger than the LLLL criterion, and, in fact, can yield better results even than the full Shearer criterion. This is possible because it does not apply in the same generality as the original LLLL; yet, it is strong enough to cover many applications of the LLLL in combinatorics. We show a variety of new bounds and algorithms. A noteworthy application is for k-SAT, with bounded occurrences of variables. As shown in Gebauer et al. [2011], a k-SAT instance in which every variable appears L ≤ 2/k+1e(k+1) times, is satisfiable. Although this bound is asymptotically tight (in k), we improve it to L ≤ 2/k+1 (1 − 1/k)kk−1 − 2/k, which can be significantly stronger when k is small. We introduce a new parallel algorithm for the LLLL. While Moser and Tardos described a simple parallel algorithm for the Lovász Local Lemma and described a simple sequential algorithm for a form of the Lopsided Lemma, they were not able to combine the two. Our new algorithm applies in nearly all settings in which the sequential algorithm works—this includes settings covered by our new, stronger LLLL criterion.

On computing maximal independent sets of hypergraphs in parallel

Whether or not the problem of finding maximal independent sets (MIS)in hypergraphs is in R NC is one of the fundamental problems in the theory of parallel computing. Unlike the well-understood case of MIS in graphs, for the hypergraph problem, our knowledge is quite limited despite considerable work. It is known that the problem is in RNC when the edges of the hypergraph have constant size. For general hypergraphs with n vertices and m edges, the fastest previously known algorithm works in time O(√‾n) with poly(m,n) processors. In this paper we give an EREW PRAM algorithm that works in time no(1) with poly(m,n) processors on general hypergraphs satisfying m<nlog(2)n⁄8(log(3)n)2, where log(2)n = log log n and log(3)n = log log log n. Our algorithm is based on a sampling idea that reduces the dimension of the hypergraph and employs the algorithm for constant dimension hypergraphs as a subroutine.

A Lottery Model for Center-Type Problems with Outliers

In this paper, we give tight approximation algorithms for the

Parallel Algorithms and Concentration Bounds for the Lovász Local Lemma via Witness DAGs

k

On Computing Maximal Independent Sets of Hypergraphs in Parallel

-center and matroid center problems with outliers. Unfairness arises naturally in this setting: certain clients could always be considered as outliers. To address this issue, we introduce a lottery model in which each client

A note on near‐optimal coloring of shift hypergraphs

j

Deterministic Parallel Algorithms for Fooling Polylogarithmic Juntas and the Lovász Local Lemma

is allowed to submit a parameter

A Constructive Lovász Local Lemma for Permutations

p_j \in [0,1]