Open-separating dominating codes in graphs

Using dominating sets to separate vertices of graphs is a well-studied problem in the larger domain of identification problems. In such problems, the objective is to choose a suitable dominating set $C$ of a graph $G$ such that the neighbourhoods of all vertices of $G$ have distinct intersections with $C$. Such a dominating and separating set $C$ is often referred to as a \emph{code} in the literature. Depending on the types of dominating and separating sets used, various problems arise under various names in the literature. In this paper, we introduce a new problem in the same realm of identification problems whereby the code, called \emph{open-separating dominating code}, or \emph{OSD-code} for short, is a dominating set and uses open neighbourhoods for separating vertices. The paper studies the fundamental properties concerning the existence, hardness and minimality of OSD-codes. Due to the emergence of a close and yet difficult to establish relation of the OSD-codes with another well-studied code in the literature called open locating dominating codes, or OLD-codes for short, we compare the two on various graph families. Finally, we also provide an equivalent reformulation of the problem of finding OSD-codes of a graph as a covering problem in a suitable hypergraph and discuss the polyhedra associated with OSD-codes, again in relation to OLD-codes of some graph families already studied in this context

On three domination numbers in block graphs

The problems of determining minimum identifying, locating-dominating or open locating-dominating codes are special search problems that are challenging both from a theoretical and a computational point of view. Hence, a typical line of attack for these problems is to determine lower and upper bounds for minimum codes in special graphs. In this work we study the problem of determining the cardinality of minimum codes in block graphs (that are diamond-free chordal graphs). We present for all three codes lower and upper bounds as well as block graphs where these bounds are attained

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set.</p> <p>Results</p> <p>We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using <it>in silico</it>-generated time-series data sets on wild-type and <it>in silico </it>mutants.</p> <p>Conclusions</p> <p>The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model.</p

Reconstructing extended Petri nets with priorities - handling priority conflicts revisited

This work aims at reconstructing Petri net models for biological systems from experimental time-series data. The reconstructed models shall reproduce the experimentally observed dynamic behavior in a simulation. For that, we consider Petri nets with priority relations among the transitions and control-arcs, to obtain additional activation rules for transitions to control the dynamic behavior. An integrative reconstruction method, taking both priority relations and control-arcs into account, was proposed by Favre and Wagler in 2013. Here, we detail the aspect of choosing priorities and control-arcs such that dynamic conflicts can be resolved to finally arrive at the experimentally observed behavior

Balancedness of subclasses of circular-arc graphs

A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, but no characterization by mininal forbidden induced subgraphs is known, not even for the case of circular-arc graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. In this work, we characterize when a given graph G is balanced in terms of minimal forbidden induced subgraphs, by restricting the analysis to the case where G belongs to certain classes of circular-arc graphs, including Helly circular-arc graphs, claw-free circular-arc graphs, and gem-free circular-arc graphs. In the case of gem-free circular-arc graphs, analogous characterizations are derived for two superclasses of balanced graphs: clique-perfect graphs and coordinated graphs.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Chile; ChileFil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Wagler, Annegret Katrin. Centre National de la Recherche Scientifique; Franci

Fleet Management for Autonomous Vehicles Using Multicommodity Coupled Flows in Time-Expanded Networks

VIPAFLEET is a framework to develop models and algorithms for managing a fleet of Individual Public Autonomous Vehicles (VIPA). We consider a homogeneous fleet of such vehicles distributed at specified stations in a closed site to supply internal transportation, where the vehicles can be used in different modes of circulation (tram mode, elevator mode, taxi mode). We treat in this paper a variant of the Online Pickup-and-Delivery Problem related to the taxi mode by means of multicommodity coupled flows in a time-expanded network and propose a corresponding integer linear programming formulation. This enables us to compute optimal offline solutions. However, to apply the well-known meta-strategy Replan to the online situation by solving a sequence of offline subproblems, the computation times turned out to be too long, so that we devise a heuristic approach h-Replan based on the flow formulation. Finally, we evaluate the performance of h-Replan in comparison with the optimal offline solution, both in terms of competitive analysis and computational experiments, showing that h-Replan computes reasonable solutions, so that it suits for the online situation

A polyhedral study of a relaxation of the routing and spectrum allocation problem

The routing and spectrum allocation (RSA) problem arises in the context of flexible grid optical networks, and consists in routing a set of demands through a network while simultaneously assigning a bandwidth to each demand, subject to non-overlapping constraints. One of the most effective integer programming formulations for RSA is the DR-AOV formulation, presented in a previous work. In this work we explore a relaxation of this formulation with a subset of variables from the original formulation, in order to identify valid inequalities that could be useful within a cutting-plane environment for tackling RSA. We present basic properties of this relaxed formulation, we identify several families of facet-inducing inequalities, and we show that they can be separated in polynomial time