Efficiently Calculating Evolutionary Tree Measures Using SAT

Bonet, María Luisa; John, Katherine St.

doi:10.1007/978-3-642-02777-2_3

Cited by 17 publications

(16 citation statements)

References 26 publications

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“…There is an approximation algorithm of ratio 3 (Hein et al 1996), as well as an ILP algorithm for calculating an exact rooted SPR distance (Wu 2009). An exact rooted SPR distance is also determined by reducing it to CNF (Bonet and John 2009) and using existing SAT solvers.…”

Section: A Review Of Previous Resultsmentioning

confidence: 99%

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

Hasic

Tannier

2019

J Comb Optim

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Phylogenetic trees illustrate the evolutionary history of genes and species. In most cases, although genes evolve along with the species they belong to, a species tree and gene tree are not identical, because of evolutionary events at the gene level like duplication or transfer. These differences are handled by phylogenetic reconciliation, which formally is a mapping between gene tree nodes and species tree nodes and branches. We investigate models of reconciliation with a gene transfer that replaces existing gene, which is a biological important event but never included in reconciliation models. Also the problem is close to a dated version of the classical subtree prune and regraft (SPR) distance problem, where a pruned subtree has to be regrafted only on a branch closer to the root. We prove that the reconciliation problem including transfer and replacement is NP-hard, and that if speciations and transfers with replacement are the only allowed evolutionary events, then it is fixed-parameter tractable (FPT) with respect to the reconciliation's weight. We prove that the results extend to the dated SPR problem.Keywords phylogenetic reconciliation · dated subtree prune and regraft SPR · gene transfer · transfer with replacement (replacing transfer) · NP hard/complete · fixed parameter tractable FPT

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Section: A Review Of Previous Resultsmentioning

confidence: 99%

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

Hasic

Tannier

2019

J Comb Optim

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“…Any subset of these pairs can be generated via the choice rule in line 4, permitting instances of edge/2 to hold without further preconditions. 1 For example, the atoms characterizing the directed graph in Figure 1(a) are edge (1,2), edge (1,3), edge (2,4), edge (3,2), edge (4,5), and edge (5,3).…”

Section: Directed Acyclic Graphsmentioning

confidence: 99%

“…For instance, Bayesian network structure learning, where directed acyclic graphs provide solution candidates, can be reduced to constraint optimization [15,28,16]. Constraint-based methods can also be used to infer phylogenetic trees [7,5], describing the evolution of living organisms, languages, and other evolving systems. Furthermore, chordal Markov network learning amounts to the task of optimizing maximum weight spanning trees induced by chordal graphs [14].…”

Section: Introductionmentioning

confidence: 99%

Declarative encodings of acyclicity properties

Gebser

Janhunen

Rintanen

2015

Journal of Logic and Computation

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Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.

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“…These formulas encode computing evolutionary tree measures into SAT [47]. The results of these instances are shown in Table 4.…”

Section: Bio-informaticsmentioning

confidence: 99%

Automated Reencoding of Boolean Formulas

Manthey

Heule

Biere

2013

Hardware and Software: Verification and Testing

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Abstract. We present a novel preprocessing technique to automatically reduce the size of Boolean formulas. This technique, called Bounded Variable Addition (BVA), exchanges clauses for variables. Similar to other preprocessing techniques, BVA greedily lowers the sum of variables and clauses, a rough measure for the hardness to solve a formula. We show that cardinality constraints (CCs) can efficiently be reencoded: from a naive CC encoding, BVA automatically generates a compact encoding, which is smaller than sophisticated encodings. Experimental results show that applying BVA can improve SAT solving performance.

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Efficiently Calculating Evolutionary Tree Measures Using SAT

Cited by 17 publications

References 26 publications

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

Declarative encodings of acyclicity properties

Automated Reencoding of Boolean Formulas

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