Michael Segal

Improved approximation algorithms for connected sensor cover

Wireless sensor networks have recently posed many new system building challenges. One of the main problems is energy conservation since most of the sensors are devices with limited battery life and it is infeasible to replenish energy via replacing batteries. An effective approach for energy conservation is scheduling sleep intervals for some sensors, while the remaining sensors stay active providing continuous service. In this paper we consider the problem of selecting a set of active sensors of minimum cardinality so that sensing coverage and network connectivity are maintained. We show that the greedy algorithm that provides complete coverage has an approximation factor no better than Ω(log n), where n is the number of sensor nodes. Then we present algorithms that provide approximate coverage while the number of nodes selected is a constant factor far from the optimal solution. Finally, we show how to connect a set of sensors that already provides coverage.

Enumerating longest increasing subsequences and patience sorting

Abstract In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1,…,n . The third problem is to enumerate all the longest monotone increasing subsequences of the given permutation.

Dynamic coverage in ad-hoc sensor networks

AbstractAd-hoc networks of sensor nodes are in general semi-permanently deployed. However, the topology of such networks continuously changes over time, due to the power of some sensors wearing out, to new sensors being inserted into the network, or even due to designers moving sensors around during a network re-design phase (for example, in response to a change in the requirements of the network). In this paper, we address the problem of how to dynamically maintain two important measures on the quality of the coverage of a sensor network: the best-case coverage and worst-case coverage distances. We assume that the ratio between upper and lower transmission power of sensors is bounded by a polynomial of n, where n is the number of sensors, and that the motion of mobile sensors can be described as a low-degree polynomial function of time. We maintain a (1+ε)-approximation on the best-case coverage distance and a

Enclosing k points in the smallest axis parallel rectangle

(\sqrt 2 + \varepsilon )

Novel algorithms for the network lifetime problem in wireless settings

-approximation on the worst-case coverage distance of the network, for any fixed ε>0. Our algorithms have amortized or worst-case poly-logarithmic update costs. We are able to efficiently maintain the connectivity of the regions on the plane with respect to the sensor network, by extending the concatenable queue data structure to also serve as a priority queue. In addition, we present an algorithm that finds the shortest maximum support path in time O(nlog n).

Mobile facility location (extended abstract)

In this paper, we study strategies for allocating and managing friendly jammers, so as to create virtual barriers that would prevent hostile eavesdroppers from tapping sensitive wireless communication. Our scheme precludes the use of any encryption technique. Applications include domains such as (i) protecting the privacy of storage locations where RFID tags are used for item identification, (ii) secure reading of RFID tags embedded in credit cards, (iii) protecting data transmitted through wireless networks, sensor networks, etc. By carefully managing jammers to produce noise, we show how to reduce the SINR of eavesdroppers to below a threshold for successful reception, without jeopardizing network performance. We present algorithms targeted towards optimizing power allocation and number of jammers needed in several settings. Experimental simulations back up our results.

Improved Competitive Performance Bounds for CIOQ Switches

We consider the following clustering problem. Given a set S of n points in the plane, and given an integer k, n2 < k ⩽ n we want to find the smallest axis parallel rectangle (smallest perimeter or area) that encloses exactly k points of S. We present an algorithm which runs in time O(n + k(n − k)2) improving previous algorithms which run in time O(k2n) and do not perform well for larger k values. We present an algorithm to enclose k of n given points in an axis parallel box in d-dimensional space which runs in time O(dn + dk(n − k)2(d − 1) and occupies O(dn) space. We slightly improve algorithms for other problems whose runtimes depend on k.

Near-optimal multicriteria spanner constructions in wireless ad hoc networks

Current network processors (NPs) increasingly deal with packets with heterogeneous processing times. In such an environment, packets that require many processing cycles delay low-latency traffic because the common approach in todays NPs is to employ run-to-completion processing. These difficulties have led to the emergence of the Multipass NP architecture, where after a processing cycle ends, all processed packets are recycled into the buffer and recompete for processing resources. In this paper, we provide a model that captures many of the characteristics of this architecture, and we consider several scheduling and buffer management algorithms that are specially designed to optimize the performance of multipass network processors. In particular, we provide analytical guarantees for the throughput performance of our algorithms. We further conduct a comprehensive simulation study, which validates our results.