( k , +)-distance-hereditary graphs

AbstractIn this work we introduce, characterize, and provide algorithmic results for (k,+)-distance-hereditary graphs, k⩾0. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k,+)-distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between these nodes in the faulty graph is bounded by the distance in the non-faulty graph plus an integer constant k. The class of all these graphs is denoted by DH(k,+). By varying the parameter k, classes DH(k,+) include all graphs and form a hierarchy that represents a parametric extension of the well-known class of distance-hereditary graphs

Mutual-visibility in distance-hereditary graphs: a linear-time algorithm

The concept of mutual-visibility in graphs has been recently introduced. If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u, v\}$. If every two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$. It is known that computing the mutual-visibility number of a graph is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and grids. In this paper, we study the mutual-visibility in distance-hereditary graphs and show that the mutual-visibility number can be computed in linear time for this class.Comment: 16 pages, 5 figures, a preliminary version will appear on the proc. of the XII Latin and American Algorithms, Graphs and Optimization Symposium, {LAGOS} 2023, Huatulco, Mexico, September 18-22, 2023. Procedia Computer Science, Elsevie

Networks with small stretch number

Abstract In a previous work, the authors introduced the class of graphs with bounded induced distance of order k (BID(k) for short), to model non-reliable interconnection networks. A network modeled as a graph in BID(k) can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between these nodes in the faulty graph is at most k times the distance in the non-faulty graph. The smallest k such that G∈BID(k) is called stretch number of G. We show an odd characteristic of the stretch numbers: every rational number greater or equal 2 is a stretch number, but only discrete values are admissible for smaller stretch numbers. Moreover, we give a new characterization of classes BID(2−1/i), i⩾1, based on forbidden induced subgraphs. By using this characterization, we provide a polynomial time recognition algorithm for graphs belonging to these classes, while the general recognition problem is Co-NP-complete

A Systematic Approach for Evaluating Satellite Communications Systems

The aerospace environment imposes straight opera- tive conditions so every electronic system usually needs to be validated for these. The same way, communica- tion systems need to be evaluated before their intro- duction in aerospace applications. In the paper we present a new methodology for the evaluation of com- munication systems in space applications. The meth- odology aims, by abstraction, at identifying all the critical aspects for the evaluation and at defining a standard and reusable framework in order to be appli- cable to any Communication Systems. The methodol- ogy has been applied for the evaluation of three Data Bus for satellite communications: 1553, 1-Wire and Profibus DP RS 485 based systems have been analyzed and evaluate

Dynamic Algorithms for Recoverable Robustness Problems

Recently, the recoverable robustness model has been introduced in the optimization area. This model allows to consider disruptions (input data changes) in a unified way, that is, during both the strategic planning phase and the operational phase. Although the model represents a significant improvement, it has the following drawback: we are typically not facing only one disruption, but many of them might appear one after another. In this case, the solutions provided in the context of the recoverable robustness are not satisfying. In this paper we extend the concept of recoverable robustness to deal not only with one single recovery step, but with arbitrarily many recovery steps. To this aim, we introduce the notion of dynamic recoverable robustness problems. We apply the new model in the context of timetabling and delay management problems. We are interested in finding efficient dynamic robust algorithms for solving the timetabling problem and in evaluating the price of robustness of the proposed solutions

Self-spanner graphs

n/

An area-efficient 2-D convolution implementation on FPGA for space applications

The 2-D Convolution is an algorithm widely used in image and video processing. Although its computation is simple, its implementation requires a high computational power and an intensive use of memory. Field Programmable Gate Arrays (FPGA) architectures were proposed to accelerate calculations of 2-D Convolution and the use of buffers implemented on FPGAs are used to avoid direct memory access. In this paper we present an implementation of the 2-D Convolution algorithm on a FPGA architecture designed to support this operation in space applications. This proposed solution dramatically decreases the area needed keeping good performance, making it appropriate for embedded systems in critical space application

Partially dynamic efficient algorithms for distributed shortest paths

n/