INTRODUCTION AND PROBLEM DESCRIPTION. In the third century of the Common Era (CE), when Rome dominated not only Europe, but also North Africa and the Near East, it was able to deploy fifty legions throughout the empire. In this forward defense strategy even the furthermost areas of the empire were secured by the on-site presence of an adequate number of legions of the Roman army. However, the empire had lost much of its muscle by the fourth century CE and the forces of Rome had diminished to only about twenty-five legions. It had thus become impossible to station legions in sufficient strength at all of the forward positions of the empire without abandoning the core. A new defense in depth strategy was devised by the Emperor Constantine (Constantine The Great, 274-337) to cope with the reduced power of the empire [11]. His defense in depth used local troops to disrupt invasion and deployed mobile Field Armies (FAs) to stop and throw back the intruding enemy, or to suppress insurrection. The earlier forward defense strategy had provided a wall around the empire denying any but the most modest of incursions-it even allowed Roman forces to sally into barbarian lands to disrupt invasions as they were being mounted. In place of Rome's forces, the defense in depth strategy substituted local part-time militias (who would be fighting for their own land and families) to slow and fragment any invading barbarian army until the heavier weight of an FA, dispatched from a distant area, could be brought to bear. Each set of roughly six legions with ancillary cavalry, artillery, etc. forms an FA, a unit of forces whose numbers are sufficient to secure any one of the regions of the empire [2]. In the third century CE, Rome's fifty legions or about eight FAs could be allocated so that each of the eight provinces was secured by its own FA. However, by the fourth century CE, only four FAs were available for deployment. The regions of the empire are considered to be connected as shown in Figure 1, where each region is represented as a circle (node). Movement along a line (edge) between regions (nodes) represents a "step" and for a region to be securable, an FA must be able to reach it in just one step [2]. A region is considered to be secured if it has one or more FAs stationed in it already. On the other hand, the region may be securable-that is, an FA may be capable of deploying to protect that region in a single step, but only under a special condition. An FA can be deployed from one region to an adjacent region only if it moves from a region where there is at least one other FA to help launch it. This is analogous to the island-hopping strategy pursued by General MacArthur in World War II in the Pacific Theater-movement followed the chain of islands already secured by troops left behind.
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