On guarding real terrains: the terrain guarding and the blocking path problems

Locating a minimum number of guards on a terrain such that every point on the terrain is guarded by at least one of the guards is known as the Terrain Guarding Problem (TGP). In this paper, a realistic example of the terrain guarding problem is studied, involving the surveillance of a rugged geographical terrain by means of thermal cameras. A number of issues related to TGP are addressed with integer-programming models proposed to solve the problem. Also, a sensitivity analysis is carried out in which five fictitious terrains are created to see the effect of the resolution of the terrain, and of terrain characteristics, on coverage optimization and the required number of guards. Finally, a new problem, which is called the Blocking Path Problem (BPP), is introduced. BPP is about guarding a path on the terrain with a minimum number of guards such that the path blocks all possible infiltration routes. A discussion is provided about the relation of BPP to the Network Interdiction Problem (NIP), which has been studied extensively by the operations research community, and to the k-Barrier Coverage Problem, which has been studied under the Sensor Deployment Problem. BPP is solved via an integer-programming formulation based on a network paradigm

A finite dominating set of cardinality O(k) and a witness set of cardinality O(n) for 1.5D terrain guarding problem

1.5 dimensional (1.5D) terrain is characterized by a piecewise linear curve. Locating minimum number of guards on the terrain (T) to cover/guard the whole terrain is known as 1.5D terrain guarding problem. Approximation algorithms and a polynomial-time approximation scheme have been presented for the problem. The problem has been shown to be NP-Hard. In the problem, the set of possible guard locations and the set of points to be guarded are uncountable. To solve the problem to optimality, a finite dominating set (FDS) of size O (n2) and a witness set of size O (n3) have been presented, where n is the number of vertices on T. We show that there exists an even smaller FDS of cardinality O (k) and a witness set of cardinality O(n), where k is the number of convex points. Convex points are vertices with the additional property that between any two convex points the piecewise linear curve representing the terrain is convex. Since it is always true that k≤ n for n≥ 2 and since it is possible to construct terrains such that n= 2 k, the existence of an FDS with cardinality O(k) and a witness set of cardinality of O (n) leads to the reduction of decision variables and constraints respectively in the zero-one integer programming formulation of the problem. © 2017, Springer Science+Business Media New York

Terrain prickliness: theoretical grounds for high complexity viewsheds

An important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union of all the triangle parts that are visible from the viewpoint. The complexity of a viewshed can vary significantly, from constant to quadratic in the number of terrain vertices, depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible perspectives. We show that the prickliness effectively captures the potential of 2.5D terrains to have high complexity viewsheds, and we present near-optimal algorithms to compute the prickliness of 1.5D and 2.5D terrains. We also report on some experiments relating the prickliness of real word 2.5D terrains to the size of the terrains and to their viewshed complexity.Peer ReviewedPostprint (author's final draft

Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains

Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains

Machara and Kodori Valleys (historical Apsilia) of NW Georgia in Caucasia in the 1st to 7th centuries AD

The dissertation concerns the historical Apsilia and offers a new theoretical approach to the nature of Apsilian material culture, which covers the period from the 1st to the early 7th centuries. Reasons are reflected in critical evaluation of the past scholarly contribution, where all problems have been analyzed. Three studies are conducted in this thesis that moves over two historical timescale Roman and early medieval periods. The author aims for her achievements and presents a background for new arguments and theories. First is a descriptive-analytical study of cremated minorities of Olginskoe cemetery. This attempts to reveal the full potential of acts, changes, and the purpose of individual choices, leading to distinctive practices and diversifying grave structures. They are patterns rarely considered in past studies of burial customs and drawing on this author’s new research, vision and imaginations. It sets out a new approach to the regional context of cremated minorities. New typo-chronology and relevant content of applied specifics (some are resistant to local origin) attempt to reconcile the components of the cultural definition (‘Tsebeldian culture’) of Apsilian material culture. They are unique components and a new context of hypothesis which can be tested in archaeological evidence. The other two issues derive from past scholarly contributions concerning the potential, perspectives, and functions of the geo-strategically significant NW region-Apsilia within Colchis/Lazica. It seeks to provide a broader understanding of the evolution of late Roman and early Byzantine Apsilian sites. This is a new approach to the study, which makes accessible the introduction of time-relative pieces of evidence and attempts to encompass existing knowledge about the studied material, but with a different perspective. It explores the possibility of new narratives by investigating broad features of trade and regional militarization that led to a global political establishment in Apsilia

Beyond the Trenches

This collection of articles is the outcome of extensive investigations into archival materials, concerning the involvement of various nations in the Great War. The authors analyse the wartime experiences of individuals and local communities, as well as whole nations. They offer a closer, more personal view of the impact of the Great War. The book re-constructs individual war narratives, and studies the long-term consequences of the conflict. The result is a multifaceted portrayal of the war, seen from local and international perspectives

Beyond the Trenches – The Social and Cultural Impact of the Great War

This collection of articles is the outcome of extensive investigations into archival materials, concerning the involvement of various nations in the Great War. The authors analyse the wartime experiences of individuals and local communities, as well as whole nations. They offer a closer, more personal view of the impact of the Great War. The book re-constructs individual war narratives, and studies the long-term consequences of the conflict. The result is a multifaceted portrayal of the war, seen from local and international perspectives