Network Resource Allocation Under Fairness Constraints

This work considers the basic problem of allocating resources among a group of agents in a network, when the agents are equipped with single-peaked preferences over their assignments. This generalizes the classical claims problem, which concerns the division of an estate's liquidation value when the total claim on it exceeds this value. The claims problem also models the problem of rationing a single commodity, or the problem of dividing the cost of a public project among the people it serves, or the problem of apportioning taxes. A key consideration in this classical literature is equity: the good (or the ``bad,'' in the case of apportioning taxes or costs) should be distributed as fairly as possible. The main contribution of this dissertation is a comprehensive treatment of a generalization of this classical rationing problem to a network setting. Bochet et al. recently introduced a generalization of the classical rationing problem to the network setting. For this problem they designed an allocation mechanism---the egalitarian mechanism---that is Pareto optimal, envy free and strategyproof. In chapter 2, it is shown that the egalitarian mechanism is in fact group strategyproof, implying that no coalition of agents can collectively misreport their information to obtain a (weakly) better allocation for themselves. Further, a complete characterization of the set of all group strategyproof mechanisms is obtained. The egalitarian mechanism satisfies many attractive properties, but fails consistency, an important property in the literature on rationing problems. It is shown in chapter 3 that no Pareto optimal mechanism can be envy-free and consistent. Chapter 3 is devoted to the edge-fair mechanism that is Pareto optimal, group strategyproof, and consistent. In a related model where the agents are located on the edges of the graph rather than the nodes, the edge-fair rule is shown to be envy-free, group strategyproof, and consistent. Chapter 4 extends the egalitarian mechanism to the problem of finding an optimal exchange in non-bipartite networks. The results vary depending on whether the commodity being exchanged is divisible or indivisible. For the latter case, it is shown that no efficient mechanism can be strategyproof, and that the egalitarian mechanism is Pareto optimal and envy-free. Chapter 5 generalizes recent work on finding stable and balanced allocations in graphs with unit capacities and unit weights to more general networks. The existence of a stable and balanced allocation is established by a transformation to an equivalent unit capacity network

Flexibly Connected Thin-walled Space Frame Stability

The elastic stability of a cubic space frame composed of cold-formed steel members is studied for various bending and warping rigidities. A finite element technique is used to perform a parametric study of the elastic stability response of the flexibly connected frame. The results are compared with previously published observations for hot-rolled steel sections. The criterion used for deciding the significance of warping for hot-rolled sections is not found to be applicable to cold-formed sections

Optimal index coding with min-max probability of error over fading channels

An index coding scheme in which the source (transmitter) transmits symbols over a wireless fading channel is considered. Index codes with the transmitter using minimum number of transmissions are known as optimal index codes. Different optimal index codes give different performances in terms of probability of error in a fading environment and this also varies from receiver to receiver. In this paper we deal with optimal index codes which minimizes the maximum probability of error among all the receivers. We identify a criterion for optimal index codes that minimizes the maximum probability of error among all the receivers. For a special class of index coding problems, we give an algorithm to identify optimal index codes which minimize the maximum error probability. We illustrate our techniques and claims with simulation results leading to conclude that a careful choice among the optimal index codes will give a considerable gain in fading channels

Single Uniprior Index Coding With Min-Max Probability of Error Over Fading Channels

An index coding scheme in which the source (transmitter) transmits symbols over a wireless fading channel is considered. Index codes with the transmitter using minimum number of transmissions are known as optimal index codes. Different optimal index codes give different performances in terms of probability of error in a fading environment, and this also varies from receiver to receiver. In this paper, we deal with optimal index codes, which minimizes the maximum probability of error among all the receivers. We identify a criterion for optimal index codes that minimizes the maximum probability of error among all the receivers. For a special class of index coding problems, we give an algorithm to identify optimal index codes whichminimize the maximum error probability. We illustrate our techniques and claims with simulation results leading to conclude that a careful choice among the optimal index codes will give a considerable gain in fading channels

Optimal Index Coding with Min-Max Probability of Error over Fading Channels

An index coding scheme in which the source (transmitter) transmits symbols over a wireless fading channel is considered. Index codes with the transmitter using minimum number of transmissions are known as optimal index codes. Different optimal index codes give different performances in terms of probability of error in a fading environment and this also varies from receiver to receiver. In this paper we deal with optimal index codes which minimizes the maximum probability of error among all the receivers. We identify a criterion for optimal index codes that minimizes the maximum probability of error among all the receivers. For a special class of index coding problems, we give an algorithm to identify optimal index codes which minimize the maximum error probability. We illustrate our techniques and claims with simulation results leading to conclude that a careful choice among the optimal index codes will give a considerable gain in fading channels