Search results for "Directed graph"
showing 10 items of 43 documents
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Distributed Adaptive Consensus Tracking Control of Uncertain High-order Nonlinear Systems under Directed Graph Condition
2018
In this paper, we investigate the output consensus tracking problem for a class of high-order nonlinear systems subjected to unknown parameters and uncertain external disturbances. A novel backstepping based distributed adaptive control scheme is presented under the directed communication status. For the subsystems without direct access to time-varying desired trajectory, local estimators are introduced and the corresponding adaptive laws are designed in a totally distributed fashion. With the presented scheme, the assumption on linearly parameterized reference signal and the information exchange operation of subsystem inputs in the existing results are no longer needed. It is shown that al…
Variable neighborhood descent for the incremental graph drawing
2017
Abstract Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edge crossing reduction in the context of incremental graph drawing, in which we want to preserve the layout of a graph over successive drawings. We propose a hybrid method based on the GRASP (Greedy Randomized Adaptive Search Procedure) and VND (Variable Neighborhood Descent) methodologies and compare it with previous methods via simulation.
Revealing community structures by ensemble clustering using group diffusion
2018
We propose an ensemble clustering approach using group diffusion to reveal community structures in data. We represent data points as a directed graph and assume each data point belong to single cluster membership instead of multiple memberships. The method is based on the concept of ensemble group diffusion with a parameter to represent diffusion depth in clustering. The ability to modulate the diffusion-depth parameter by varying it within a certain interval allows for more accurate construction of clusters. Depending on the value of the diffusion-depth parameter, the presented approach can determine very well both local clusters and global structure of data. At the same time, the ability …
Geometric interpretation of the optimality conditions in multifacility location and applications
1991
Geometrical optimality conditions are developed for the minisum multifacility location problem involving any norm. These conditions are then used to derive sufficient conditions for coincidence of facilities at optimality; an example is given to show that these coincidence conditions seem difficult to generalize.
An algorithm for the Rural Postman problem on a directed graph
1986
The Directed Rural Postman Problem (DRPP) is a general case of the Chinese Postman Problem where a subset of the set of arcs of a given directed graph is ‘required’ to be traversed at minimum cost. If this subset does not form a weakly connected graph but forms a number of disconnected components the problem is NP-Complete, and is also a generalization of the asymmetric Travelling Salesman Problem. In this paper we present a branch and bound algorithm for the exact solution of the DRPP based on bounds computed from Lagrangean Relaxation (with shortest spanning arborescence sub-problems) and on the fathoming of some of the tree nodes by the solution of minimum cost flow problems. Computation…
Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies
2022
In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforcing this constraint remains unclear, although it has been hypothesized to be implemented by the connectivity of the sampled neurons. We test this idea and explore the interactions between local synaptic connectivity and its ability to encode information in a lower dimensional manifold through simulations of a detailed microcircuit model with realistic sources of noise. We confirm that even in isolation such a model can encode the identity of different stimuli in a lo…
Two Parallel Algorithms for the Analysis of Random Images
1988
Aim of the paper is to show a computational paradigm, that reduces some algorithms on undirected graphs into image analysis algorithms. In particular two parallel algorithms on undirected weighted graphs, often used in the analysis of sparse images, are described.
Energy Efficient Consensus Over Directed Graphs
2018
Consensus algorithms are iterative methods that represent a basic building block to achieve superior functionalities in increasingly complex sensor networks by facilitating the implementation of many signal-processing tasks in a distributed manner. Due to the heterogeneity of the devices, which may present very different capabilities (e.g. energy supply, transmission range), the energy often becomes a scarce resource and the communications turn into directed. To maximize the network lifetime, a magnitude that in this work measures the number of consensus processes that can be executed before the first node in the network runs out of battery, we propose a topology optimization methodology fo…
Evaluating the structure and use of hiking trails in recreational areas using a mixed GPS tracking and graph theory approach
2014
Abstract Recreational trails encourage numerous outdoor leisure activities in a variety of urban, rural, and natural environments. Understanding the way trails function is crucial for the designers and managers of recreational sites to balance the needs of visitors and site capacities. This paper presents a new approach to evaluate the structure and use of hiking trails by combining GPS tracking and analytical methods based on graph theory. The study is based upon empirical data (N = 482 GPS tracks) collected in the Lobau, which is part of the Danube Floodplains National Park in Austria. The physical structure of trails (structural network; undirected graph) and their usage (functional netw…