Linear search with terrain-dependent speeds

We revisit the linear search problem where a robot, initially placed at the origin on an infinite line, tries to locate a stationary tar-get placed at an unknown position on the line. Unlike previous studies, in which the robot travels along the line at a constant speed, we con-sider settings where the robot’s speed can depend on the direction of travel along the line, or on the profile of the terrain, e.g. when the line is inclined, and the robot can accelerate. Our objective is to design search algorithms that achieve good competitive ratios for the time spent by the robot to complete its search versus the time spent by an omniscient robot that knows the location of the target. We consider several new robot mobility models in which the speed of the robot depends on the terrain. These include (1) different con-stant speeds for different directions, (2) speed with constant acceleration and/or variability depending on whether a certain segment has already been searched, (3) speed dependent on the incline of the terrain. We pro-vide both upper and lower bounds on the competitive ratios of search algorithms for these models, and in many cases, we derive optimal algo-rithms for the search time

Weak coverage of a rectangular barrier

Assume n wireless mobile sensors are initially dispersed in an ad hoc manner in a rectangular region. They are required to move to final locations so that they can detect any intruder crossing the region in a direction parallel to the sides of the rectangle, and thus provide weak bar-rier coverage of the region. We study three optimization problems related to the movement of sensors to achieve weak barrier coverage: minimizing the number of sensors moved (MinNum), minimizing the average distance moved by the sensors (MinSum), and minimizing the maximum distance moved by the sensors (

Approximate hotlink assignment

Consider a directed rooted tree T=(V,E) of maximal degree d representing a collection V of web pages connected via a set E of links all reachable from a source home page, represented by the root of T. Each leaf web page carries a weight representative of the frequency with which it is visited. By adding hotlinks, shortcuts from a node to one of its descendents, we are interested in minimizing the expected number of steps needed to visit the leaf pages from the home page. We give an O(N2) time algorithm for assigning hotlinks so that the expected number of steps to reach the leaves from the root of the tree is at most H(p)/(log(d+1)-(d/(d+1))logd)+(d+1)/d, where H(p) is the entropy of the probability (frequency) distribution p=〈p1,p 2,⋯,pN〉 on the N leaves of the given tree, i.e., pi is the weight on the ith leaf. The best known lower bound for this problem is H(p)/log(d+1). We also show how to adapt our algorithm to complete trees of a given degree d and in this case we prove it is optimal, asymptotically in d

Routing and Scheduling I/O Transfers on Wormhole-Routed Mesh Networks

This paper addresses the problem of routing and scheduling parallel I/O operations to minimize the time required to transfer data between processors and I/O devices. In particular, 2-dimensional Mesh is considered in which routing is performed using wormhole switching, and I/O nodes are placed on the periphery of the mesh. Within this context, two kinds of scheduling mechanisms are studied. In the first, packets may be blocked temporarily in the network: an algorithm is presented that allocates routes based on minimizing traffic congestion on the interconnection network. In the second, a scheduling algorithm which ensures that no packet will blocked along its route is presented. This paper discusses the complexity of these problems, proposes and evaluates several heuristic algorithms, and experimentally compares the performance of blocking and non-blocking routing techniques. 1 Introduction The time required for I/O operations is known to often severely limit the performance of a par..

Priority evacuation from a disk: The case of n = 1,2,3

An exit (or target) is at an unknown location on the perimeter of a unit disk. A group of n+1 robots (in our case, n=1,2,3), initially located at the centre of the disk, are tasked with finding the exit. The robots have unique identities, share the same coordinate system, move at maximum speed 1 and are able to communicate wirelessly the position of the exit once found. Among them there is a distinguished robot called the queen and the remainder of the robots are referred to as servants. It is known that with two robots searching, the room can be evacuated (i.e., with both robots reaching the exit) in [Formula presented] time units and this is optimal [11]. Somewhat surprisingly, in this paper we show that if the goal is to have the q

Complexity of barrier coverage with relocatable sensors in the plane

We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: the feasibility of barrier coverage, the problem of minimizing the largest relocation distance of a sensor (MinMax), and the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the problems are shown to be NP-complete. We also study the case when sensors use perpendicular movem

Complexity of barrier coverage with relocatable sensors in the plane

We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area of fixed range centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: (i) the feasibility of barrier coverage, (ii) the problem of minimizing the largest relocation distance of a sensor (MinMax), and (iii) the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the MinMax problem is shown to be strongly NP-complete for sensors with arbitrary ranges. We also study the case when sensors are restricted to use perpendicular movement to one of the barriers. We show that when the barriers are parallel, both the MinMax and MinSum problems can be solved in polynomial time. In contrast, we show that even the feasibility problem is strongly NP-complete if two perpendicular barriers are to be covered, even if the sensors are located at integer positions, and have only two possible sensing ranges. On the other hand, we give an O(n3/2) algorithm for a natural special case of this last problem