On optimal realizations of finite metric spaces by graphs
Discrete & Computational Geometry
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Inferring evolutionary trees with strong combinatorial evidence
Theoretical Computer Science - computing and combinatorics
Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
The complexity of checking consistency of pedigree information and related problems
Journal of Computer Science and Technology - Special issue on bioinformatics
Phylogenetic Super-Networks from Partial Trees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Compatibility of unrooted phylogenetic trees is FPT
Theoretical Computer Science - Parameterized and exact computation
Inferring a level-1 phylogenetic network from a dense set of rooted triplets
Theoretical Computer Science - Computing and combinatorics
The maximum agreement of two nested phylogenetic networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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In this paper, we study a problem of inferring blood relationships which satisfy a given matrix of genetic distances between all pairs of n nodes. Blood relationships are represented by our proposed graph class, which is called a pedigree graph. A pedigree graph is a directed acyclic graph in which the maximum indegree is at most two. We show that the number of pedigree graphs which satisfy the condition of given genetic distances may be exponential, but they can be represented by one directed acyclic graph with n nodes. Moreover, an O(n3) time algorithm which solves the problem is also given. Although phylogenetic trees and phylogenetic networks are similar data structures to pedigree graphs, it seems that inferring methods for phylogenetic trees and networks cannot be applied to infer pedigree graphs since nodes of phylogenetic trees and networks represent species whereas nodes of pedigree graphs represent individuals. We also show an O(n2) time algorithm which detects a contradiction between a given pedigree graph and distance matrix of genetic distances.