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14
Links Between Maximum Likelihood and Maximum Parsimony Under a Simple Model of Site Substitution
, 1997
"... Stochastic models of nucleotide substitution are playing an increasingly important role in phylogenetic reconstruction through such methods as maximum likelihood. Here we examine the behaviour of a simple substitution model and establish some links between the methods of maximum parsimony and maximu ..."
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Cited by 83 (13 self)
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Stochastic models of nucleotide substitution are playing an increasingly important role in phylogenetic reconstruction through such methods as maximum likelihood. Here we examine the behaviour of a simple substitution model and establish some links between the methods of maximum parsimony and maximum likelihood under this model. 1
Coloring Away Communication in Parallel Query Optimization
, 1995
"... We address the problem of finding parallel plans for SQL queries using the twophase approach of join ordering and query rewrite (JOQR) followed by parallelization. We focus on the JOQR phase and develop optimization algorithms that account for communication as well as computation costs. Using a mod ..."
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Cited by 30 (1 self)
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We address the problem of finding parallel plans for SQL queries using the twophase approach of join ordering and query rewrite (JOQR) followed by parallelization. We focus on the JOQR phase and develop optimization algorithms that account for communication as well as computation costs. Using a model based on representing the partitioning of data as a color, we devise an efficient algorithm for the problem of choosing the partitioning attributes in a query tree so as to minimize total cost. We extend our model and algorithm to incorporate the interaction of data partitioning with conventional optimization choices such as access methods and strategies for computing operators. Our algorithms apply to queries that include operators such as grouping, aggregation, intersection and set difference in addition to joins.
Minimizing communication costs of distributed local computation
, 2005
"... A valuation algebra offers a suitable framework to represent knowledge and information. Based on this framework, several algorithms to process knowledge and pooled under the name local computation were mapped out in recent years. This paper proposes an extension of the valuation algebra framework th ..."
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A valuation algebra offers a suitable framework to represent knowledge and information. Based on this framework, several algorithms to process knowledge and pooled under the name local computation were mapped out in recent years. This paper proposes an extension of the valuation algebra framework that allows to express the costs of transmitting valuations between network hosts. Based on this model, we estimate the total computation costs caused by the local computation architectures and observe under which constraints these costs can be minimized. Once a sufficient condition is identified, we present an
Generalized Buneman Pruning for Inferring the Most Parsimonious Multistate Phylogeny
, 2010
"... Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NPhard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in ..."
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Cited by 2 (1 self)
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Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NPhard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worstcase running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multistate maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multistate problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multistate data sets of more than a few characters.
INFINITE COMBINATORICS: FROM FINITE TO INFINITE
"... Abstract. We investigate the relationship between some theorems in finite combinatorics and their infinite counterparts: given a “finite ” result how one can get an “infinite ” version of it? We will also analyze the relationship between the proofs of a “finite” theorem and the proof of its “infinit ..."
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Abstract. We investigate the relationship between some theorems in finite combinatorics and their infinite counterparts: given a “finite ” result how one can get an “infinite ” version of it? We will also analyze the relationship between the proofs of a “finite” theorem and the proof of its “infinite ” version. Besides these comparisons, the paper gives a proof of a theorem of Erdős, Grünwald and Vázsonyi giving the full descriptions of graphs having one/twoway infinite Euler lines. The last section contains some new results: an infinite version of a multiwaycut theorem is included. 1.
Exactly Computing the Parsimony Scores on Phylogenetic Networks Using Dynamic Programming
, 2014
"... Scoring a given phylogenetic network is the first step that is required in searching for the best evolutionary framework for a given dataset. Using the principle of maximum parsimony, we can score phylogenetic networks based on the minimum number of state changes across a subset of edges of the netw ..."
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Scoring a given phylogenetic network is the first step that is required in searching for the best evolutionary framework for a given dataset. Using the principle of maximum parsimony, we can score phylogenetic networks based on the minimum number of state changes across a subset of edges of the network for each character that are required for a given set of characters to realize the input states at the leaves of the networks. Two such subsets of edges of networks are interesting in light of studying evolutionary histories of datasets: (i) the set of all edges of the network, and (ii) the set of all edges of a spanning tree thatminimizes the score. The problems of finding the parsimony scores under these two criteria define slightly different mathematical problems that are both NPhard. In this article, we show that both problems, with scores generalized to adding substitution costs between states on the endpoints of the edges, can be solved exactly using dynamic programming. We show that our algorithms require O(mpk) storage at each vertex (per character), where k is the number of states the character can take, p is the number of reticulate vertices in the network,m = k for the problem with edge set (i), andm = 2 for the problem with edge set (ii). This establishes an O(nmpk2) algorithm for both the problems (n is the number of leaves in the network), which are extensions of Sankoffâs algorithm for finding the parsimony scores for phylogenetic trees. We will discuss improvements in the complexities and show that for phylogenetic networks whose underlying undirected graphs have disjoint cycles, the storage at each vertex can be reduced to O(mk), thus making the algorithm polynomial for this class of networks. We will present some properties of the two approaches and guidance on choosing between the criteria, as well as traverse through the network space using either of the definitions. We show that our methodology provides an effective means to study a wide variety of datasets.
On a bidirected relaxation for the MULTIWAY CUT problem
 Discrete Applied Math
, 2005
"... In the Multiway Cut problem, we are given an undirected edgeweighted graph G = (V;E) with c e denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to nd a minimum cost set of edges whose removal ensures that the terminals are dis ..."
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In the Multiway Cut problem, we are given an undirected edgeweighted graph G = (V;E) with c e denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to nd a minimum cost set of edges whose removal ensures that the terminals are disconnected. In this paper, we study a bidirected linear programming relaxation of Multiway Cut. We resolve an open problem posed by Vazirani [10], and show that the integrality gap of this relaxation is no better than that for a geometric linear programming relaxation given by Calinescu et al. [2], and may be strictly worse on some instances. 1
Maximum Lifetime Continuous Query Processing in Wireless Sensor Networks
, 2010
"... Monitoring applications emerge as one of the most important applications of wireless sensor networks (WSNs). Such applications typically have long–running complex queries that are continuously evaluated over the sensor measurement streams. Due to the limited energy of the sensors in WSNs, energy eff ..."
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Monitoring applications emerge as one of the most important applications of wireless sensor networks (WSNs). Such applications typically have long–running complex queries that are continuously evaluated over the sensor measurement streams. Due to the limited energy of the sensors in WSNs, energy efficient query evaluation is critical to prolong the system lifetime — the earliest time that the network can not perform its intended task anymore. We model complex queries by expression trees and consider the problem of maximizing the lifetime of a wireless sensor network for the continuous in–network evaluation of an expression trees T, so the value of its root is available at the base station. In–network evaluation means that the evaluation of the operators of T may be pushed to the network nodes, and continuous means the repeated evaluation of T (once at each round). Continuous in–network evaluation of T entails addressing the following two coupled aspects of the problem: (a) the placement of the operators, variables, and constants of T to network nodes, and (b) the routing of their values to the appropriate network nodes that needed them to evaluate the operators. We analyze the complexity and provide a simple and effective algorithm for the placement of the nodes of T onto the sensor nodes of a WSN. Our algorithm of operator placement attempts to minimize the total amount of data that need to be communicated. A placement of T induces a certain Maximum Lifetime Concurrent–Flow (MLCF) problem. We provide an efficient algorithm that finds near–optimal integral solutions to the MLCF problem, where a solution is a collection of paths on which certain amount of integral flow is routed. Our approach to the continuous in–network evaluation of T consists of utilizing both our placement and routing algorithms above.