scholarly journals A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Schaller ◽  
Marc Hellmuth ◽  
Peter F. Stadler
Keyword(s):  
Phylogenetic Trees ◽  
Linear Time ◽  
Time Algorithm ◽  
Input Tree ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Asymptotically Optimal ◽  
The Common ◽  
Mathematical Phylogenetics ◽  
Special Case

Abstract Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

scholarly journals Permutation Pattern matching in (213, 231)-avoiding permutations

2017 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Both Neou ◽  
Romeo Rizzi ◽  
Stéphane Vialette
Keyword(s):  
Pattern Matching ◽  
Related Problem ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Matching Problem ◽  
Permutation Pattern ◽  
Special Case ◽  
Longest Subsequence

Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm. We extend our research to bivincular patterns that avoid 213 and 231 and present a O(kn 4)-time algorithm. Finally we look at the related problem of the longest subsequence which avoids 213 and 231.

scholarly journals TESTING MUTUAL DUALITY OF PLANAR GRAPHS

2014 ◽  
Vol 24 (04) ◽  
pp. 325-346 ◽  
Author(s):  
PATRIZIO ANGELINI ◽  
THOMAS BLÄSIUS ◽  
IGNAZ RUTTER
Keyword(s):  
Planar Graphs ◽  
Linear Time ◽  
Dual Graph ◽  
Time Algorithm ◽  
Equivalence Classes ◽  
Self Duality ◽  
Dual Relation ◽  
The Common ◽  
Special Case ◽  
Np Hardness

We introduce and study the problem MUTUAL DUALITY, asking for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. We show NP-completeness for general planar graphs and give a linear-time algorithm for biconnected planar graphs. This algorithm implies an efficient solution to two well-known problems. In fact, it can be used to test whether two biconnected planar graphs are 2-isomorphic, namely whether their graphic matroids are isomorphic, and to test self-duality of any biconnected planar graph, which is a special case of MUTUAL DUALITY with G1 = G2. Further, we show that our NP-hardness proof extends to testing self-duality and map self-duality (which additionally requires to preserve the embedding). In order to obtain our results, we consider the common dual relation ~, where G1 ~ G2 if and only if they admit embeddings that result in the same dual graph. We show that ~ is an equivalence relation on the set of biconnected graphs and devise a compact SPQR-tree-like representation of its equivalence classes. Our algorithm for biconnected graphs is based on testing isomorphism for two such representations in linear time.

scholarly journals A Linear-Time Algorithm for the Isometric Reconciliation of Unrooted Trees

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 225
Author(s):  
Broňa Brejová ◽  
Rastislav Královič
Keyword(s):  
Family History ◽  
Gene Family ◽  
Phylogenetic Trees ◽  
Evolutionary History ◽  
Linear Time ◽  
Gene Tree ◽  
Time Algorithm ◽  
Species Tree ◽  
Linear Time Algorithm ◽  
History Of

In the reconciliation problem, we are given two phylogenetic trees. A species tree represents the evolutionary history of a group of species, and a gene tree represents the history of a family of related genes within these species. A reconciliation maps nodes of the gene tree to the corresponding points of the species tree, and thus helps to interpret the gene family history. In this paper, we study the case when both trees are unrooted and their edge lengths are known exactly. The goal is to root them and to find a reconciliation that agrees with the edge lengths. We show a linear-time algorithm for finding the set of all possible root locations, which is a significant improvement compared to the previous O(N3logN) algorithm.

scholarly journals OPTIMAL ALGORITHMS FOR SUBSTRATE TESTING IN MULTI-CHIP MODULES

1995 ◽  
Vol 06 (04) ◽  
pp. 595-612 ◽  
Author(s):  
ANDREW B. KAHNG ◽  
GABRIEL ROBINS ◽  
ELIZABETH A. WALKUP
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Fault Coverage ◽  
Traveling Salesman ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Open Problems ◽  
Empirical Results ◽  
Technical Challenges ◽  
Actual Substrate

Multi-chip module (MCM) packaging techniques present several new technical challenges, notably substrate testing. We formulate MCM substrate testing as a problem of connectivity verification in trees via k-probes, and present a linear-time algorithm which computes a minimum set of probes achieving complete open fault coverage. Since actual substrate testing also involves scheduling probe operations, we formulate efficient probe scheduling as a special type of metric traveling salesman optimization and give a provably-good heuristic. Empirical results using both random and industry benchmarks demonstrate reductions in testing costs of up to 21% over previous methods. We conclude with generalizations to alternate probe technologies and several open problems.

scholarly journals A linear-time algorithm to sample the dual-birth model

2017 ◽  
Author(s):  
Niema Moshiri
Keyword(s):  
Phylogenetic Trees ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Sampling Algorithm

AbstractThe ability to sample models of tree evolution is essential in the analysis and interpretation of phylogenetic trees. The dual-birth model is an extension of the traditional birth-only model and allows for sampling trees of varying degrees of balance. However, for a tree with n leaves, the tree sampling algorithm proposed in the original paper is 𝒪(n log n). I propose an algorithm to sample trees under the dual-birth model in 𝒪(n), and I provide a fast C++ implementation of the proposed algorithm.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

Sign in / Sign up

Export Citation Format

Share Document