Trade relations between the Mycenaean Greeks and the civilizations of the Eastern Mediterranean in the Late Bronze Age

The Mycenaean Greeks are often assumed to have been in contact with the civilizations of the Mediterranean throughout the Late Bronze Age. The extent of this contact however is not as clearly understood, and the archaeological evidence that has survived provides a sample of what must have exchanged hands. This thesis will examine the archaeological, textual and iconographic evidence from a number of sites and sources, from the Anatolian plains to the Kingdom of Egypt and major settlements in-between during the Late Bronze Age to examine what trade may have looked like for the Mycenaeans. Due to the extensive finds in some regions and a lack of evidence in others, this paper will also try to understand the relationship between the Mycenaeans and other cultures to determine whether a trade embargo was enacted on the Mycenaeans by the Central Anatolian Hittites during this period, or whether other factors contributed to the paucity of objects in Central Anatolia.

Efficient algorithms for beacon routing in polygons

In a paper by Biro et al. [7], a novel twist on guarding in art galleries is introduced. A beacon is a fixed point with an attraction pull that can move points within the polygon. Points move greedily to monotonically decrease their Euclidean distance to the beacon by moving straight towards the beacon or sliding on the edges of the polygon. The beacon attracts a point if the point eventually reaches the beacon. Unlike most variations of the art gallery problem, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. For a given point in the polygon, the inverse attraction region is the set of beacon locations that can attract the point. We first study the characteristics of beacon attraction. We consider the quality of a "successful" beacon attraction and provide an upper bound of $\sqrt{2}$ on the ratio between the length of the beacon trajectory and the length of the geodesic distance in a simple polygon. In addition, we provide an example of a polygon with holes in which this ratio is unbounded. Next we consider the problem of computing the shortest beacon watchtower in a polygonal terrain and present an $O(n \log n)$ time algorithm to solve this problem. In doing this, we introduce $O(n \log n)$ time algorithms to compute the beacon kernel and the inverse beacon kernel in a monotone polygon. We also prove that $\Omega(n \log n)$ time is a lower bound for computing the beacon kernel of a monotone polygon. Finally, we study the inverse attraction region of a point in a simple polygon. We present algorithms to efficiently compute the inverse attraction region of a point for simple, monotone, and terrain polygons with respective time complexities $O(n^2)$, $O(n \log n)$ and $O(n)$. We show that the inverse attraction region of a point in a simple polygon has linear complexity and the problem of computing the inverse attraction region has a lower bound of $\Omega(n \log n)$ in monotone polygons and consequently in simple polygons.