Resource allocation in communication networks aims to assign various resources such as power, bandwidth and load in a fair and economic fashion so that the networks can be better utilized and shared by the communicating entities. The design of efficient resource-allocation algorithms is, however, becoming more and more challenging due to the precipitously increasing scale of the networks. This thesis strives to understand how to design such low-complexity algorithms with performance guarantees.

In the first part, the link scheduling problem in wireless ad hoc networks is considered. The scheduler is charge of finding a set of wireless data links to activate at each time slot with the considerations of wireless interference, traffic dynamics, network topology and quality-of-service (QoS) requirements. Two different yet essential scenarios are investigated: the first one is when each packet has a specific deadline after which it will be discarded; the second is when each packet traverses the network in multiple hops instead of leaving the network after a one-hop transmission. In both scenarios the links need to be carefully scheduled to avoid starvation of users and congestion on links. One greedy algorithm is analyzed in each of the two scenarios and performance guarantees in terms of throughput of the networks are derived.

In the second part, the load-balancing problem in parallel computing is studied. Tasks arrive in batches and the duty of the load balancer is to place the tasks on the machines such that minimum queueing delay is incurred. Due to the huge size of modern data centers, sampling the status of all machines may result in significant overhead. Consequently, an algorithm based on limited queue information at the machines is examined and its asymptotic delay performance is characterized and it is shown that the proposed algorithm achieves the same delay with remarkably less sampling overhead compared to the well-known power-of-two-choices algorithm.

Two messages of the thesis are the following: greedy algorithms can work well in a stochastic setting; the fluid model can be useful in "derandomizing" the system and reveal the nature of the algorithm.