Tracking strategies for mobile users in wireless networks are studied. In order to save the cost of using the wireless links mobile users should not update their location whenever they cross boundaries of adjacent cells. The paper focuses on three natural strategies in which the mobile users make the decisions when and where to update: the time-based strategy, the number of movements-based strategy, and the distance-based strategy. The authors consider both memoryless movement patterns and movements with Markovian memory along a topology of cells arranged as a ring. They analyze the performance of each one of the three strategies under such movements, and show the performance differences between the strategies.>

Tracking strategies for mobile wireless networks are studied, assuming a cellular architecture where base stations interconnected by a wired network communicate with mobile units via wireless links. The cost of utilizing the wireless links for the actual tracking of mobile users is investigated. A tracking strategy in which a subset of all base stations is selected and designated as reporting centers is proposed. Mobile users transmit update messages only upon entering cells of reporting centers, while every search for a mobile user is restricted to the vicinity of the reporting center to which the user last reported. It is shown that for an arbitrary topology of the cellular network (represented by the interference graph), finding an optimal set of reporting centers is an NP-complete problem. Optimal and near-optimal solutions for important special cases of the interference graph are given.>

Tracking strategies for mobile wireless networks are studied. A cellular architecture in which base stations that are interconnected by a wired network communicate with mobile units via wireless links is assumed. The cost of utilizing the wireless links for the actual tracking of mobile users is considered. A tracking strategy in which a subset of all base stations is selected and designed as reporting centers is proposed. Mobile users transmit update messages only upon entering cells of reporting centers, while every search for a mobile user is restricted to the vicinity of the reporting center to which the user last reported. It is shown that, for an arbitrary topology of the cellular network (represented by the mobility graph), finding an optimal set of reporting centers is an NP-complete problem. Optimal and near-optimal solutions for important special cases of the mobility graph are presented.>

A class of binary trees that grow in a random environment, where the state of the environment can change at every vertex of the trees, is studied. The trees considered are single-type and two-type binary trees that grow in a two-state Markovian environment. For each kind of tree, the conditions on the environment process for extinction of the tree are determined, and the problem of calculating the expected number of vertices of the tree is addressed. Different ways of growing the trees are compared.>

The impact of fairness on the throughput of ring networks with spatial reuse is investigated. A model for a slotted ring with spatial reuse that employs a simple fairness mechanism is presented. An exact expression for the expected time taken to evacuate this ring when each node initially contains one packet is derived. The expected evacuation time is used to obtain an exact expression for the throughput of the ring. It is shown that as the number of nodes on the ring increases, the penalty for fairness in terms of throughput becomes negligible.>

Algorithms for the group testing problem when there is no a priori information on the number of defective items are considered. The efficiency criterion used in the competitive ratio, which is the ratio of the number of tests required by an algorithm when there is no a priori information on the number of defective items, to the number of tests required by an optimal algorithm when the number of defective items is known in advance. A new algorithm is presented, and it is shown that the competitive ratio of this algorithm is 2. This result is an improvement over an algorithm given by D.Z. Du et al. (1991), for which the competitive ratio was 2.75. It also proves a conjecture made by them. A new application of group testing techniques for high-speed networks is discussed.>

A study is made of a class of binary trees that grow in a random environment, where the state of the environment can change at every vertex of the trees. Such trees arise in multiaccess communication. The trees considered are single-type and two-type binary trees that grow in a two-state Markovian environment. For each kind of tree, the conditions on the environment process for extinction of the tree are determined, and the problem of calculating the expected number of vertices of the tree is addressed. Different ways of growing the trees are compared.>

Multiaccess networks in which the shared channel is noisy are considered. A slotted-time collision-type channel, Poisson infinite-user model, and a ternary feedback are assumed. Due to the noise in the shared channel, the received signal may be detected as a collision event though no message or a single message is transmitted. This kind of imperfect feedback is referred to as an error. A common assumption in all previous studies of multiaccess algorithms in channels with errors is that the channel is memoryless. The problem of splitting algorithms when the channel is with memory is considered here. A two-state first-order Markovian model for the channel is introduced and the operation of the tree collision resolution algorithm in this channel is analyzed. A stability result, i.e. the necessary conditions on the channel parameters for stability conditions hold, the throughput of the algorithm is calculated. Extensions to more general channel models are discussed.>

Multi-access networks are considered in which the shared channel is noisy. The authors assume a slotted-time collision-type channel, Poisson infinite-user model, and binary feedback. Due to the noise in the shared channel, the received signal may be detected as a collision even though no message or a single message is transmitted. This kind of imperfect feedback is referred to as error. A common assumption in all previous studies of multi-access algorithms in channels with errors is that the channel is memoryless. The authors consider the problem of splitting algorithms when the channel has memory. They introduce a two-state, first-order Markovian model for the channel and analyze the operation of the tree collision-resolution algorithm in this channel. They obtain a stability result, i.e., the necessary conditions on the channel parameters for stability of the algorithm. Assuming that the stability conditions hold, they calculate the throughput of the algorithm. Assuming that the stability conditions hold, they calculate the throughput of the algorithm. Extensions to more general channel moders are discussed.>

Algorithms for accessing a slotted-time collision-type broadcast are considered under a Poisson infinite-user model, where each user observes the channel and determines for each slot whether idle or success or collision has occurred. The highest throughput previously achieved for this model is 0.4878. A new scheme is introduced which does not exceed the limitations of the system model, yet achieves a throughput of 0.4892. Extra information is added to the message that can be used only when the message is received successfully. One form of extra information is described, and a new algorithm that exploits it is proposed.>