Query-points visibility constraint minimum link paths in simple polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links

On Romeo and Juliet Problems: Minimizing Distance-to-Sight

We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points s and t in a simple polygon P with no holes, we want to minimize the distance these persons travel in order to see each other in P. We solve two variants of this problem, one minimizing the longer distance the two persons travel (min-max) and one minimizing the total travel distance (min-sum), optimally in linear time. We also consider a query version of this problem for the min-max variant. We can preprocess a simple n-gon in linear time so that the minimum of the longer distance the two persons travel can be computed in O(log^2 n) time for any two query positions where the two persons lie

Geometric Secluded Paths and Planar Satisfiability

We consider paths with low exposure to a 2D polygonal domain, i.e., paths which are seen as little as possible; we differentiate between integral exposure (when we care about how long the path sees every point of the domain) and 0/1 exposure (just counting whether a point is seen by the path or not). For the integral exposure, we give a PTAS for finding the minimum-exposure path between two given points in the domain; for the 0/1 version, we prove that in a simple polygon the shortest path has the minimum exposure, while in domains with holes the problem becomes NP-hard. We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT

MAPPA. Methodologies applied to archaeological potential Predictivity

The fruitful cooperation over the years between the university teaching staff of Univerità di Pisa (Pisa University), the officials of the Soprintendenza per i Beni Archeologici della Toscana (Superintendency for Archaeological Heritage of Tuscany), the officials of the Soprintendenza per i Beni Architettonici, Paesaggistici, Artistici ed Etnoantropologici per le Province di Pisa e Livorno (Superintendency for Architectural, Landscape and Ethno-anthropological Heritage for the Provinces of Pisa and Livorno), and the Comune di Pisa (Municipality of Pisa) has favoured a great deal of research on issues regarding archaeological heritage and the reconstruction of the environmental and landscape context in which Pisa has evolved throughout the centuries of its history. The desire to merge this remarkable know-how into an organic framework and, above all, to make it easily accessible, not only to the scientific community and professional categories involved, but to everyone, together with the wish to provide Pisa with a Map of archaeological potential (the research, protection and urban planning tool capable of converging the heritage protection needs of the remains of the past with the development requirements of the future) led to the development of the MAPPA project – Methodologies applied to archaeological potential predictivity - funded by Regione Toscana in 2010. The two-year project started on 1 July 2011 and will end on 30 June 2013. The first year of research was dedicated to achieving the first objective, that is, to retrieving the results of archaeological investigations from the archives of Superintendencies and University and from the pages of scientific publications, and to making them easily accessible; these results have often never been published or have often been published incompletely and very slowly. For this reason, a webGIS (“MappaGIS” that may freely accessed at http://mappaproject.arch.unipi.it/?page_id=452) was created and will be followed by a MOD (Mappa Open Data archaeological archive), the first Italian archive of open archaeological data, in line with European directives regarding access to Public Administration data and recently implemented by the Italian government also (the beta version of the archive can be viewed at http://mappaproject.arch.unipi.it/?page_id=454). Details are given in this first volume about the operational decisions that led to the creation of the webGIS: the software used, the system architecture, the organisation of information and its structuring into various information layers. But not only. The creation of the webGIS also gave us the opportunity to focus on a series of considerations alongside the work carried out by the MAPPA Laboratory researchers. We took the decision to publish these considerations with a view to promoting debate within the scientific community and, more in general, within the professional categories involved (e.g. public administrators, university researchers, archaeology professionals). This allowed us to overcome the critical aspects that emerged, such as the need to update the archaeological excavation documentation and data archiving systems in order to adjust them to the new standards provided by IT development; most of all, the need for greater and more rapid spreading of information, without which research cannot truly progress. Indeed, it is by comparing and connecting new data in every possible and, at times, unexpected way that research can truly thrive