Extracting few representative reconciliations with Host-Switches (Extended Abstract)

Phylogenetic tree reconciliation is the approach commonly used to in- vestigate the coevolution of sets of organisms such as hosts and symbionts. Given a phylogenetic tree for each such set, respectively denoted by H and S, together with a mapping φ of the leaves of S to the leaves of H, a reconciliation is a mapping ρ of the internal vertices of S to the vertices of H which extends φ with some constraints. Given a cost for each reconciliation, a huge number of most parsimonious ones are possible, even exponential in the dimension of the trees. Without further information, any biological interpretation of the underlying coevolution would require that all optimal solutions are enumerated and examined. The latter is however impossible without pro- viding some sort of high level view of the situation. One approach would be to extract a small number of representatives, based on some notion of similarity or of equivalence between the reconciliations. In this paper, we define two equivalence relations that allow one to identify many reconciliations with a single one, thereby reducing their number. Extensive experiments indicate that the number of output solutions greatly decreases in general. By how much clearly depends on the constraints that are given as input

A Realistic Model to Support Rescue Operations after an Earthquake via UAVs

In this paper, we consider the problem of completely flying over an area just hit by an earthquake with a fleet of Unmanned Aerial Vehicles (UAVs) to opportunely direct rescue teams. The cooperation between UAVs ensures that the search for possible survivors can be faster and more effective than the solutions currently implemented by civil protection. To study this scenario, we introduce the Cover by Multitrips with Priorities (CMP) problem, which tries to keep into account all the main real-life issues connected to the flight and coordination of the UAVs. We conduct a theoretical study to estimate the best number of UAVs and additional batteries, to give indications to the organization that leads the rescue teams to be able to guarantee rapid and effective rescue. Finally, based on some theoretical considerations, we propose some heuristics that tackle the problem of flying over the whole area with a fleet of UAVs in the shortest possible time. Simulations show that they work efficiently in both the proposed scenarios and provide better performance than previous solutions once they are arranged to work in our scenarios. The main advantages of our approach w.r.t. the current drone-based solutions used by the civil defense are that UAVs do not need drivers so the time of all available rescue workers can be invested in doing something else. In our model, we take into account that some sites (e.g. buildings with a high fire risk or schools and hospitals) have a higher priority and must be inspected first, and the possibility that UAVs can make a decision based on what they detect. Finally, our approach allows UAVs to collaborate so that the same sites will be flown over exactly once in order to speed up the rescue mission

Algorithms for the quantitative Lock/Key model of cytoplasmic incompatibility

Cytoplasmic incompatibility (CI) relates to the manipulation by the parasite Wolbachia of its host reproduction. Despite its widespread occurrence, the molecular basis of CI remains unclear and theoretical models have been proposed to understand the phenomenon. We consider in this paper the quantitative Lock-Key model which currently represents a good hypothesis that is consistent with the data available. CI is in this case modelled as the problem of covering the edges of a bipartite graph with the minimum number of chain subgraphs. This problem is already known to be NP-hard, and we provide an exponential algorithm with a non trivial complexity. It is frequent that depending on the dataset, there may be many optimal solutions which can be biologically quite different among them. To rely on a single optimal solution may therefore be problematic. To this purpose, we address the problem of enumerating (listing) all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time. Interestingly, in order to solve the above problems, we considered also the problem of enumerating all the maximal chain subgraphs of a bipartite graph and improved on the current results in the literature for the latter. Finally, to demonstrate the usefulness of our methods we show an application on a real dataset

Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms

The Min Energy broadcast problem consists in assigning transmission ranges to the nodes of an ad-hoc network in order to guarantee a directed spanning tree from a given source node and, at the same time, to minimize the energy consumption (i.e. the energy cost) yielded by the range assignment. Min energy broadcast is known to be NP-hard. We consider random-grid networks where nodes are chosen independently at random from the $n$ points of a $\sqrt n \times \sqrt n$ square grid in the plane. The probability of the existence of a node at a given point of the grid does depend on that point, that is, the probability distribution can be non-uniform. By using information-theoretic arguments, we prove a lower bound $(1-\epsilon) \frac n{\pi}$ on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than $1.1204 \frac n{\pi}$. Finally, we present a fully-distributed protocol that constructs a broadcast range assignment of energy cost not larger than $8n$,thus still yielding constant approximation. The energy load is well balanced and, at the same time, the work complexity (i.e. the energy due to all message transmissions of the protocol) is asymptotically optimal. The completion time of the protocol is only an $O(\log n)$ factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least $1-1/n^{\Theta(1)}$.Comment: 13 pages, 3 figures, 1 tabl

A Book of Generations – Writing at the Frontier

We address the problem of finding viewpoints that preserve the relational structure of a three-dimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint “goodness” were proposed. Unfortunately, the inherent combinatorial complexity of the problem makes finding exact solutions is impractical. In this paper, we propose two approximation algorithms for the problem, commenting on their design, and presenting results on their performance

Upward Three-Dimensional Grid Drawings of Graphs

A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. We prove that every $n$-vertex graph with bounded degeneracy has a three-dimensional grid drawing with $O(n^{3/2})$ volume. This is the broadest class of graphs admiting such drawings. A three-dimensional grid drawing of a directed graph is \emph{upward} if every arc points up in the z-direction. We prove that every directed acyclic graph has an upward three-dimensional grid drawing with $(n^3)$ volume, which is tight for the complete dag. The previous best upper bound was $O(n^4)$. Our main result is that every $c$-colourable directed acyclic graph ($c$ constant) has an upward three-dimensional grid drawing with $O(n^2)$ volume. This result matches the bound in the undirected case, and improves the best known bound from $O(n^3)$ for many classes of directed acyclic graphs, including planar, series parallel, and outerplanar