Testing the agreement of trees with internal labels

Background A semi-labeled tree is a tree where all leaves as well as, possibly, some internal nodes are labeled with taxa. Semi-labeled trees encompass ordinary phylogenetic trees and taxonomies. Suppose we are given a collection $${\mathcal {P}}= \{{\mathcal {T}}_1, {\mathcal {T}}_2, \ldots , {\mathcal {T}}_k\}$$ P = { T 1 , T 2 , … , T k } of semi-labeled trees, called input trees, over partially overlapping sets of taxa. The agreement problem asks whether there exists a tree $${\mathcal {T}}$$ T , called an agreement tree, whose taxon set is the union of the taxon sets of the input trees such that the restriction of $${\mathcal {T}}$$ T to the taxon set of $${\mathcal {T}}_i$$ T i is isomorphic to $${\mathcal {T}}_i$$ T i , for each $$i \in \{1, 2, \ldots , k\}$$ i ∈ { 1 , 2 , … , k } . The agreement problems is a special case of the supertree problem, the problem of synthesizing a collection of phylogenetic trees with partially overlapping taxon sets into a single supertree that represents the information in the input trees. An obstacle to building large phylogenetic supertrees is the limited amount of taxonomic overlap among the phylogenetic studies from which the input trees are obtained. Incorporating taxonomies into supertree analyses can alleviate this issue. Results We give a $${\mathcal {O}}(n k (\sum _{i \in [k]} d_i + \log ^2(nk)))$$ O ( n k ( ∑ i ∈ [ k ] d i + log 2 ( n k ) ) ) algorithm for the agreement problem, where n is the total number of distinct taxa in $${\mathcal {P}}$$ P , k is the number of trees in $${\mathcal {P}}$$ P , and $$d_i$$ d i is the maximum number of children of a node in $${\mathcal {T}}_i$$ T i . Conclusion Our algorithm can aid in integrating taxonomies into supertree analyses. Our computational experience with the algorithm suggests that its performance in practice is much better than its worst-case bound indicates.

Reaching a Group-Agreement in Finite Time Under Acyclic Interaction Topology

This paper discusses the finite time agreement problem of networks with acyclic partition topology. In view of the structural characteristics of such network topology, mathematical induction is particularly suitable to prove the main conclusions in the paper. In addition, for the consideration of the finite time consensus problem, in addition to using basic matrix theory to verify the solution of the problem, this brief also has a more detailed analysis of the time required to reach consensus. Based on these two points, it is observed that the solution of this problem is due to the features of acyclic partition interactions and the continuity of the related finite time protocol and contributes to the research on the grouping consensus of multiagent system. Furthermore, simulation examples are presented to verify the theoretical results.

Testing the Agreement of Trees with Internal Labels

Background: A semi-labeled tree is a tree where all leaves as well as, possibly, some internal nodes are labeledwith taxa. Semi-labeled trees encompass ordinary phylogenetic trees and taxonomies. Suppose we are given a collection P = {T1, T2, . . . , Tk} of semi-labeled trees, called input trees, over partially overlapping sets of taxa. The agreement problem asks whether there exists a tree T , called an agreement tree, whose taxon set is the union of the taxon sets of the input trees such that the restriction of T to the taxon set of Ti is isomorphic to i, for each i ε 1, 2, . . . , k . The agreement problems is a special case of the supertree problem, the problem of synthesizing a collection of phylogenetic trees with partially overlapping taxon sets into a single supertree that represents the information in the input trees. An obstacle to building large phylogenetic supertrees is the limited amount of taxonomic overlap among the phylogenetic studies from which the input trees are obtained. Incorporating taxonomies into supertree analyses can alleviate this issue. Results: We give a O(nk(i∈[k]di + log2(nk))) algorithm for the agreement problem, where n is the total number of distinct taxa in P, k is the number of trees in P, and di is the maximum number of children of a node in Ti. Our computational experience with the algorithm suggests that its performance in practice is much better than its worst-case bound indicates.

Higher-order cluster consensus of a multi-agent network with continuous-time dynamics

This paper studies the higher-order cluster agreement problem for continuous-time networks evolving over any given directed graph. Necessary and sufficient conditions are derived to reach clusters that are not pre-determined as opposed to existing literature. The analysis shows that appropriate stabilizing choices of coupling strengths do not affect the number of clusters and the final values of the clusters. The results are verified by numerical examples.

Reaching Reliable and Trustworthy Agreement in a Multiple Damage Vehicular Ad Hoc Network

The era of Internet of Things (IoT) has begun to evolve and with this the devices around us are getting more and more connected. Vehicular Ad-hoc NETworks (VANETs) is one of the applications of IoT. VANET allow vehicles within these networks to communicate effectively with each another. VANETs can provide an extensive range of applications that support and enhance passenger safety and comfort. It is important that VANETs are applied within a safe and reliable network topology; however, the challenging nature of reaching reliable and trustworthy agreement in such distributed systems is one of the most important issues in designing a fault-tolerant system. Therefore, protocols are required so that systems can still be correctly executed, reaching agreement on the same values in a distributed system, even if certain components in the system fail. In this study, the agreement problem is revisited in a VANET with multiple damages. The proposed protocol allows all fault-free nodes (vehicles) to reach agreement with minimal rounds of message exchanges, and tolerates the maximal number of allowable faulty components in the VANET.

Fault-Diagnosis and Decision Making Algorithm for Determining Faulty Nodes in Malicious Networks

This chapter addresses fault diagnosis agreement problem in a network with malicious members. The authors provide a new algorithm to reach an agreement among fault-free members about the faulty ones. The algorithm is designed for fully-connected networks and also can be easily adapted to partially connected networks. The authors contribution is to reduce bit complexity of Byzantine agreement process by detecting the same list of faulty units in all fault-free members. Therefore, the malicious units can be removed from other consensus processes. Also, each healthy unit detects a list of malicious units locally which results in lower packet transmission in the network. The authors provided algorithm solves fault diagnosis agreement problem in 2t+1 rounds and O(nt+1) bit complexity for each member.