Median computation in graphs using consensus strategies

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review ofalgorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed.majority strategy;consensus strategy;Hill climbing median computation

Transit functions on graphs (and posets)

The notion of transit function is introduced to present a unifying approachfor results and ideas on intervals, convexities and betweenness in graphs andposets. Prime examples of such transit functions are the interval function I andthe induced path function J of a connected graph. Another transit function isthe all-paths function. New transit functions are introduced, such as the cutvertextransit function and the longest path function. The main idea of transitfunctions is that of ‘transferring’ problems and ideas of one transit functionto the other. For instance, a result on the interval function I might suggestsimilar problems for the induced path function J. Examples are given of howfruitful this transfer can be. A list of Prototype Problems and Questions forthis transferring process is given, which suggests many new questions and openproblems.graph theory;betweenness;block graph;convexity;distance in graphs;interval function;path function;induced path;paths and cycles;transit function;types of graphs

On a special class of median algebras

International audienceIn this short note we consider a class of median algebras, called (1, 2 : 3)-semilattices, that is pertaining to cluster analysis. Such median algebras arise from a natural generalization of conservativeness, and their description is given in terms of forbidden substructures

Arrow Type Impossibility Theorems over Median Algebras

We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a product A 1 x...x An of median algebras to a median algebra B are possible if and only if B is a tree, when thought of as an ordered structure

Arrow Type Impossibility Theorems over Median Algebras

We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a product A 1 x...x An of median algebras to a median algebra B are possible if and only if B is a tree, when thought of as an ordered structure

Median computation in graphs using consensus strategies

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review of algorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed

Transit functions on graphs (and posets)

The notion of transit function is introduced to present a unifying approach for results and ideas on intervals, convexities and betweenness in graphs and posets. Prime examples of such transit functions are the interval function I and the induced path function J of a connected graph. Another transit function is the all-paths function. New transit functions are introduced, such as the cutvertex transit function and the longest path function. The main idea of transit functions is that of ‘transferring’ problems and ideas of one transit function to the other. For instance, a result on the interval function I might suggest similar problems for the induced path function J. Examples are given of how fruitful this transfer can be. A list of Prototype Problems and Questions for this transferring process is given, which suggests many new questions and open problems