Mutual Visibility Research Articles

Mutual and total mutual visibility in hypercube-like graphs

Let G be a graph and X⊆V(G). Then, vertices x and y of G are X-visible if there exists a shortest x,y-path where no internal vertices belong to X. The set X is a mutual-visibility set of G if every two vertices of X are X-visible, while X is a total mutual-visibility set if any two vertices from V(G) are X-visible. The cardinality of a largest mutual-visibility set (resp. total mutual-visibility set) is the mutual-visibility number (resp. total mutual-visibility number) μ(G) (resp. μt(G)) of G. It is known that computing μ(G) is an NP-complete problem, as well as μt(G). In this paper, we study the (total) mutual-visibility in hypercube-like networks (namely, hypercubes, Fibonacci cubes, cube-connected cycles, and butterflies). Concerning computing μ(G), we provide approximation algorithms for hypercubes, Fibonacci cubes and cube-connected cycles, while we give an exact formula for butterflies. Concerning computing μt(G) (in the literature, already studied in hypercubes), whereas we obtain exact formulae for both cube-connected cycles and butterflies.

Fault-tolerant mutual visibility without any axis agreement in presence of mobility failure

We aim to solve the mutual visibility problem using N autonomous, indistinguishable, homogeneous, oblivious and opaque point robots in the presence of mobility failure. The faulty robot cannot move when it becomes faulty, but the light remains working. Initially, from any arbitrary configuration, the problem of mutual visibility using robots aims to reach a configuration where any two robots can see each other. The challenge is to reach to such a configuration in the presence of faulty robots along with obstructed visibility under which two robots see each other only if the line segment joining them does not have any robots. Every robot operates in the conventional Look-Compute-Move cycles. Robots neither have any agreement in their coordinate system nor have the knowledge of N. The problem is not solvable for a specific symmetric initial configuration of the robots. We propose an algorithm that tolerates f(≤N) number of faulty robots and uses a constant number of colors in the FSYNC setting. To be specific, the algorithm requires 21 colors and runs in O(N2) synchronous rounds. We present another algorithm much simpler than the prior one but can tolerate a single faulty robot. This algorithm needs only 2 colors in the SSYNC and 5 colors in the ASYNC setting.

Mutual visibility of luminous robots despite angular inaccuracy

We initiate the study of the Mutual Visibility problem using N opaque luminous point robots that have inaccurate movements. Each robot operates in Look-Compute-Move cycles and has a persistent light attached to it to have a weak form of communication between robots using a constant number of colors. The inaccuracy for a robot r is an angular deviation from its target point T to a point T′ such that the angle ∠TrT′<90∘. The problem becomes unsolvable if this angle is ≥90∘. From any initial configuration of the robots on the Euclidean plane, the problem aims to arrange the robots in a configuration such that any two robots are visible to each other. We assume that the robots agree on one coordinate axis. We present two collision-free algorithms, a 2 color algorithm (which is optimal in the number of colors used) for semi-synchronous setting and a 3 color algorithm for asynchronous setting, both of which run in O(N) epochs. We also study the problem in the presence of mobile faulty robots. A robot can exhibit both mobility failure and angular inaccuracies in its movement. We present a fault-tolerant algorithm that aims to bring the robots in a configuration where no three non-faulty robots are collinear, and no faulty robot lies between two non-faulty robots. This algorithm uses 10 colors and takes O(N) epochs under asynchronous settings.

The geodesic mutual visibility problem: Oblivious robots on grids and trees

The Mutual Visibility is a well-known problem in the context of mobile robots. For a set of n robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robots are collinear. For robots moving on graphs, we consider the Geodesic Mutual Visibility (GMV) problem. Robots move along the edges of the graph, without collisions, so as to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means that there is a shortest path (i.e., a “geodesic”) between each pair of robots along which no other robots reside. We study this problem in the context of trees and (finite or infinite) square grids, for robots operating under the standard Look–Compute–Move model. In both scenarios, we provide resolution algorithms along with formal correctness proofs, highlighting the most relevant peculiarities arising within the different contexts, while optimizing the time complexity.

“Hearing with the eyes” visual hearing in (a trio) music rehearsals

ABSTRACT Making music together relies, among other things, on the mutual hearing amongst co-performers and on the visual monitoring of each other’s actions and gestures. This is better facilitated when musicians share a mutual visual space where hearing and seeing play a primary role. However, drawing from workplace studies, linguistic anthropology, anthropology of the senses and multimodal interactional studies of sensoriality, we observed how mutual visibility was (tacitly) more important for coordination among musicians than they themselves were willing to admit. Thanks to the video recording of trio rehearsals, by experimentally suspending the sense of hearing, often regarded as a predominant sense in the playing of a musical instrument and to make music together, we realized that mutual visibility not only enables musicians to notice pertinent/relevant visual cues and professional gestures, but also to make sound visible and then audible, activating what we call visual hearing, a specific hybrid sense, that we captured in action.

SimVGNets: Similarity-Based Visibility Graph Networks for Carbon Price Forecasting

In response to global warming, carbon trading market emerges to reduce carbon emissions. However, uncertain fluctuations and complicated price mechanisms in the market have changed the characteristics of carbon data. Existing methods cannot track underlying structures among carbon data streams, failing to explain high variations and predict carbon prices accurately. In this case, how to predict carbon price is a problem demanding new and prompt solutions. Unlike existing predictive mechanisms with fixed structure, in this work, we investigate carbon price from a novel perspective of visibility graph networks, developing a variant forecasting framework based on visible relationships. Firstly, carbon prices are mapped into networks where data are transformed into corresponding nodes utilizing visibility algorithm. Then a novel similarity index is proposed to measure similarity distribution of nodes converted from carbon data, which extracts past and recent price information rather than only considering recent input, resulting in the loss of past knowledge. The forecasting model is finally established based on mutual visibility machamism and similarity of constructed carbon network. To verify the proposed method, experiments are conducted on real carbon datasets, and the results demonstrate the method is superior to existing models, suggesting the predictive potentials of graph network science. It is hoped that this work can act as a bridge between carbon data and networks, motivating further research on carbon price forecasting from graph network views.

Mutual visibility by fat robots with slim omnidirectional camera

In the existing literature of the Mutual Visibility problem for autonomous robot swarms, the adopted visibility models have some idealistic assumptions that are not consistent with practical sensing device implementations. This paper investigates the problem in the more realistic visibility model called opaque fat robots with slim omnidirectional camera. The robots are modeled as unit disks, each having an omnidirectional camera represented as a disk of smaller size. The region obstructed by a single robot in this model is a truncated infinite cone. This makes the visibility model significantly challenging compared to the previous ones. We assume that the robots have compasses that allow agreement in the direction and orientation of both axes of their local coordinate systems. The robots are equipped with visible lights which serve as a medium of communication and also as a form of memory. We present a distributed algorithm for the Mutual Visibility problem which is provably correct in the semi-synchronous setting. Our algorithm also provides a solution for Leader Election which we use as a subroutine in our main algorithm. Although Leader Election is trivial with two axis agreement in the full visibility model, it is challenging in our case and is of independent interest.

IEEE AP-S Volunteers in the Spotlight! [Editor’s Comments

Many of us as members of IEEE AP-S have the opportunity to benefit from the many activities, benefits, sponsorships, and conferences that AP-S has to offer every year. We owe all of this to the many volunteers in our society that support IEEE AP-S with their enthusiasm and commitment at the local, regional, national, and international levels. A central role of this dynamism is the mutual visibility of the different scales, with local activities that are publicized and honored worldwide and international initiatives that are disseminated locally to make sure that everybody knows the great opportunities that our IEEE Society has to offer. The magazine has traditionally served with enthusiasm this dynamic, and we will keep doing so even further with a brand new column that starts in this issue, “AP-S Committees & Activities.” The column’s mission is to present in one place all the upcoming and vibrant initiatives sprouting from our volunteers locally and globally. This will include AdCom activities, AP-S committees’ work and reports, local Chapter news, conference outcomes and reports, and every other relevant initiative from all of those that animate so enthusiastically our Society! I hope you will enjoy this new column, and if you have not done so already, consider volunteering for IEEE AP-S!

Evaluation of a Candidate Site in the Tibetan Plateau towards the Next Generation Event Horizon Telescope

In order to enhance the imaging capabilities of the Event Horizon Telescope (EHT) and capture the first black hole movies, the next-generation EHT (ngEHT) team is building new stations. Most stations of the EHT and ngEHT project are located in the Western Hemisphere, leaving a large vacancy in the Eastern Hemisphere. Located in the center of the Eastern Hemisphere, the Tibetan Plateau is believed to have excellent sites for (sub)millimeter astronomical radio observations. Building a telescope here could help to fill this vacancy. In this study, we evaluated the meteorological conditions of a candidate site (Shigatse, hereafter SG) with good astronomical infrastructure for this telescope. The evaluation results show that the precipitable water vapor (PWV) values of the SG site are lower than 4 mm during winter and spring, comparable to those of some existing EHT stations, and the zenith transmittances at 230 GHz and 345 GHz during March and April are excellent. We simulated VLBI observations of Sgr A* and M87 based on the conditions of the SG site and those of other existing/planned (sub)millimeter telescopes with mutual visibility at 230 GHz. The results demonstrated that images of Sgr A* and M87 could be well reconstructed, indicating that the SG site is a good candidate for future EHT/ngEHT observations.

On the mutual visibility in Cartesian products and triangle-free graphs

Given a graph G=(V(G),E(G)) and a set P⊆V(G), the following concepts have been recently introduced: (i) two elements of P are mutually visible if there is a shortest path between them without further elements of P; (ii)P is a mutual-visibility set if its elements are pairwise mutually visible; (iii) the mutual-visibility number of G is the cardinality of any largest mutual-visibility set. In this work we continue to investigate about these concepts. We first focus on mutual-visibility in Cartesian products. For this purpose, too, we introduce and investigate independent mutual-visibility sets. In the very special case of the Cartesian product of two complete graphs the problem is shown to be equivalent to the well-known Zarenkiewicz’s problem. We also characterize the triangle-free graphs with the mutual-visibility number equal to 3.

Visibility analysis of boundary layer transition

We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs are constructed from each time series. The latter are, thus, transformed into a geometrical object, whose main features can be explored using measures typical of network science that provide a reduced order representation of the underlying flow properties. Using these metrics, we observe the evolution of the flow from laminarity to turbulence and the effects exerted by the free-stream turbulence. Different from other methods requiring an extensive amount of spatiotemporal data (e.g., full velocity field) or a set of parameters and thresholds arbitrarily chosen by the user, the present network-based approach is able to identify the onset markers for transition by means of the streamwise velocity time-series alone.

Mutual visibility on grid by asynchronous luminous robots

For a team of autonomous opaque point robots on the plane, the Mutual Visibility problem asks for a distributed algorithm that allows the robots to reposition themselves, without colliding, to a configuration where they all can see each other, i.e., no three of them are collinear. In this paper, we investigate the problem on a grid based terrain where the movements of the robots are restricted only along the grid lines and only to a neighboring grid point in each step. The robots operate in Look-Compute-Move cycles under an asynchronous scheduler. They have no agreement in coordinate system and do not know the total number of robots in the team. We assume the luminous robots model where each robot is equipped with an externally visible light which can assume a constant number of predefined colors. These colors serve both as memory and as a form of communication. We give an algorithm that solves the problem from any initial configuration using 9 colors.

Mutual visibility in graphs

Let G=(V,E) be a graph and P⊆V a set of points. Two points are mutually visible if there is a shortest path between them without further points. P is a mutual-visibility set if its points are pairwise mutually visible. The mutual-visibility number of G is the size of any largest mutual-visibility set. In this paper we start the study about this new invariant and the mutual-visibility sets in undirected graphs. We introduce the Mutual-Visibility problem which asks to find a mutual-visibility set with a size larger than a given number. We show that this problem is NP-complete, whereas, to check whether a given set of points is a mutual-visibility set is solvable in polynomial time. Then we study mutual-visibility sets and mutual-visibility numbers on special classes of graphs, such as block graphs, trees, grids, tori, complete bipartite graphs, cographs. We also provide some relations of the mutual-visibility number of a graph with other invariants.

Data-driven framework for the adaptive exit selection problem in pedestrian flow: Visual information based heuristics approach

Pedestrian behavior during evacuation has been formulated using various arbitrary microscopic methods to investigate the performance of crowd dynamics while their custom rules result in low visual realism in simulation due to the complexity of intrinsic decision logic of human. Statistical analysis is an effective way to reveal the motion pattern and path planning behavior of pedestrians whose main idea is to approach the trajectory and social attributes data of pedestrians extracted from evacuation drills as much as possible. In this study, we present a data-driven based microscopic pedestrian-simulation model with continuous-space representation to explore the potential of integrating empirical analysis into crowd simulation to enhance the authenticity of decision making. This method extracts the pedestrian’s decision mode and smoothly applies it in the crowd dynamics model. Instead of navigating agents by arbitrary regulations, the desired direction of pedestrians during the motion is arranged by machine learning (ML) algorithms. The path decision module trained with actual pedestrian data improves the compatibility of the model in the application of various spatial scenarios and no longer suffers from tedious parameter fine-tuning work. To completely describe the information precepted by pedestrians, a polygon segmentation module is developed to divide the visual field of pedestrians and identify the mutual visibility among them. This module filters out the information that can be perceived by pedestrians in real situations, thereby bridges the gap between statistical analysis and numerical simulation methods. We compare different ML approaches for route-choice behavior prediction and discuss the relative importance of its influencing variables under different scenarios. Inferring the perception of social interactions from disaggregate choice data, the scope of effectiveness of conformity behavior and crowd-aversion are also discussed. The simulation results are compared with experimental data, illustrating the model’s capability to accurately reproduce the observed flow motion in various scenarios with moderate modification in physical environment initialization.

Guided Visibility Sampling++

Visibility computation is a common problem in the field of computer graphics. Examples include occlusion culling, where parts of the scene are culled away, or global illumination simulations, which are based on the mutual visibility of pairs of points to calculate lighting. In this paper, an aggressive from-region visibility technique called Guided Visibility Sampling++ (GVS++) is presented. The proposed technique improves the Guided Visibility Sampling algorithm through improved sampling strategies, thus achieving low error rates on various scenes, and being over four orders of magnitude faster than the original CPU-based Guided Visibility Sampling implementation. We present sampling strategies that adaptively compute sample locations and use ray casting to determine a set of triangles visible from a flat or volumetric rectangular region in space. This set is called a potentially visible set (PVS). Based on initial random sampling, subsequent exploration phases progressively grow an intermediate solution. A termination criterion is used to terminate the PVS search. A modern implementation using the Vulkan graphics API and RTX ray tracing is discussed. Furthermore, we show optimizations that allow for an implementation that is over 20 times faster than a naive implementation.

Optimal trajectory planning for cinematography with multiple Unmanned Aerial Vehicles

This paper presents a method for planning optimal trajectories with a team of Unmanned Aerial Vehicles (UAVs) performing autonomous cinematography. The method is able to plan trajectories online and in a distributed manner, providing coordination between the UAVs. We propose a novel non-linear formulation for this challenging problem of computing multi-UAV optimal trajectories for cinematography; integrating UAVs dynamics and collision avoidance constraints, together with cinematographic aspects like smoothness, gimbal mechanical limits and mutual camera visibility. We integrate our method within a hardware and software architecture for UAV cinematography that was previously developed within the framework of the MultiDrone project; and demonstrate its use with different types of shots filming a moving target outdoors. We provide extensive experimental results both in simulation and field experiments. We analyze the performance of the method and prove that it is able to compute online smooth trajectories, reducing jerky movements and complying with cinematography constraints.

Aerial Multi-Camera Robotic Jib Crane

A formulation based on a team of unmanned aerial vehicles operating as a fully articulated multi-camera jib crane is proposed for the application of aerial cinematography. An optimization-based controller commands the formation to follow an artistic trajectory defined by the director of photography, while actively avoiding collisions and cameras' mutual visibility. The proposed scheme, based on the cluster-space formulation, presents an intuitive way of maneuvering the virtual camera fixture while automatically adjusting the motions by imposing artistic and safety constraints, facilitating the operator task.

Mutual visibility and interaction: staff reactions to the ‘healing architecture’ of psychiatric inpatient wards in Denmark

Psychiatric hospitals are increasingly designed to reflect contemporary models of care. As such, inpatient settings are changing based on the promise that the built environment will promote patient recovery and support psychiatric work. While extant literature examines how such novel designs mediate health outcomes and shape patient experiences, less attention has been directed towards staff experiences and the mediating role of the built environment for staff/patient interaction. By focusing on the nursing station at two inpatient wards of a new, purpose-built psychiatric hospital in Denmark, this study shows that the transparent properties of the built environment produce an environment of uncertainty and distance instead of intelligibility and closeness, which in turn shapes the nature of staff/patient interaction according to a differential field of visibilities. This study indicates that greater attention must be directed towards analysing the impact of novel designs on the relational dynamics between spaces, visibilities and people to appreciate how, and for whom, the built environment makes a difference in practice. This study thus contributes to the literature on the unique characteristics of psychiatric inpatient settings and how such settings impact psychiatric staff.

Multi-scale analysis of residential behaviour based on UWB indoor positioning system-a case study of retired household in Beijing, China

ABSTRACTThis paper proposes a data acquisition and analysis workflow and framework to clarify the daily residential behaviour of occupants based on the UWB indoor positioning system. The daily activities are analysed in different scales, namely grid level, convex polygon level and room level. At the first level, how long occupants stay in each 1 m*1 m grid was calculated, so that areas occupants stay longer was obtained. In the convex polygon level, the structure of the spatial network was clarified through analysis of the properties of each zone and weight of their connections. Although the network dynamically changes when the users and time differ, general patterns can be captured through analysis of large amounts of data. In the room level, which is the common analysing units, we get the movements between rooms and analysed the room-based behavioural networks of family members. Based on the findings in three levels, new variables were introduced in a regression model, and mutual visibility is found to significantly affect the household’s behaviour. By introducing the high-resolution indoor positioning system and the network analysis most used in the urban and social studies, this research provides a new prospect of data collecting and analysis of occupant indoor behaviour.

Radiosity Model and Compensation Theorem

In the preceding conference contribution called “Radiative Heat Transfer in Buildings”, a general model for radiative heat transfer in inner spaces of buildings has been developed. The model is capable of determining radiosities, heat fluxes and heat flows with each surface of the interior. In closed spaces like interiors, the radiative energy should be conserved so that the total heat flow should be zero. This property may be formulated as the compensation theorem and should be mirrored in each reasonable model. Thus, it is desirable to verify whether our developed model satisfies such a property. The mathematical proof has been presented which has confirmed that the developed model obeys the compensation theorem. As a numerical illustration, radiative heat flows in a simple room have been computed and their total sum has been quantified and shown that this summation leads to zero value. The numerical illustrations start with formulating matrix of view factors that describe the ‘mutual visibility’ of interior surfaces and in this way they assist to redistribute radiative heat among the interior surfaces. As soon as the matrix of view factors is established, the system of algebraic equations is formed. These equations serve for computing surface radiosities. The radiosities enable estimating heat fluxes and heat flows occurring in the interior. Some of the heat flows are positive and some are negative. The positive value of heat flow means that the corresponding surface emits energy into the interior whereas the negative value indicates that the corresponding surface absorbs energy from the interior. By summing the positive and negative values of heat flows, the total heat flow can be obtained whose value is zero in agreement with the compensation theorem.