A median graph is a connected graph, such that for any three vertices u, v, w there is exactly one vertex x that lies simultaneously on a shortest (u, v)-path, a shortest (v,w)-path and a shortest (w, u)path. Examples of median graphs are trees, grids and hypercubes. We introduce and study a generalisation of tree decompositions, to be called median decompositions, where instead of decomposing ...

Models without an explicit time dependence, called singular models, are widely used for fitting the distribution of temperatures at which water droplets freeze. In 1950 Levine developed the original singular model. His key assumption was that each droplet contained many nucleation sites, and that freezing occurred due to the nucleation site with the highest freezing temperature. The fact that f...

Sea level rise has serious consequences for harbor infrastructure, storm drains and sewer systems, and many other issues. Adapting to sea level rise requires comparing different possible adaptation strategies, comparing the cost of different actions (including no action), and assessing where and at what point in time the chosen strategy should be implemented. All these decisions must be made un...

Let i (G) be the number of induced i-cubes of a graph G. Then the cubes polynomial c(G; x) of G is introduced as P i0 i (G)x i. It is shown that any function f with two related, natural properties, is up to the factor f(K 1 ; x) the cubes polynomial. The derivation @ G of a median graph G is also introduced and it is proved that the cubes polynomial is the only function f with the property f 0 ...

Abstract The general problem in location theory deals with functions that find sites on a graph (discrete case) or network (continuous case) in such a way as to minimize some cost (or maximize some benefit) to a given set of clients represented by vertices on the graph or points on the network. The axiomatic approach seeks to uniquely distinguish, by using a list of intuitively pleasing axioms,...

This work proposes a reversible data hiding algorithm that is based on the median difference histogram. The method divides the cover image into non-overlapping identical blocks. In each block, the median pixel is selected to calculate absolute differences between the median pixel value and the values of the other pixels. Then, these differences are used to generate a histogram and the histogram...

The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. ...

The circular median problem in the Double-Cut-and-Join (DCJ) distance asks to find, for three given genomes, a fourth circular genome that minimizes the sum of the mutual distances with the three other ones. This problem has been shown to be NP-complete. We show here that, if the number of vertices of degree 3 in the breakpoint graph of the three input genomes is fixed, then the problem is trac...

Demange (2012) generalized the classical singlecrossing property to the intermediate property on median graphs and proved that the representative voter theorem still holds for this more general framework. We complement her result with proving that the linear orders of any profile which is intermediate on a median graph form a Condorcet domain. We prove that for any median graph there exists a p...

Let M, A, S, and P, be the sets of median graphs, almost-median graphs, semi-median graphs and partial cubes, respectively. Then M ⊂ A ⊂ S ⊂ P. It is proved that a partial cube is almost-median if and only if it contains no convex cycle of length greater that four. This extends the result of Brešar [2] who proved that the same property characterizes almost-median graphs within the class of semi...