Makespan Minimization via Posted Prices

We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms

Feedback Allocation For OFDMA Systems With Slow Frequency-domain Scheduling

We study the problem of allocating limited feedback resources across multiple users in an orthogonal-frequency-division-multiple-access downlink system with slow frequency-domain scheduling. Many flavors of slow frequency-domain scheduling (e.g., persistent scheduling, semi-persistent scheduling), that adapt user-sub-band assignments on a slower time-scale, are being considered in standards such as 3GPP Long-Term Evolution. In this paper, we develop a feedback allocation algorithm that operates in conjunction with any arbitrary slow frequency-domain scheduler with the goal of improving the throughput of the system. Given a user-sub-band assignment chosen by the scheduler, the feedback allocation algorithm involves solving a weighted sum-rate maximization at each (slow) scheduling instant. We first develop an optimal dynamic-programming-based algorithm to solve the feedback allocation problem with pseudo-polynomial complexity in the number of users and in the total feedback bit budget. We then propose two approximation algorithms with complexity further reduced, for scenarios where the problem exhibits additional structure.Comment: Accepted to IEEE Transactions on Signal Processin

Derandomization of Online Assignment Algorithms for Dynamic Graphs

This paper analyzes different online algorithms for the problem of assigning weights to edges in a fully-connected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear over time. Performance of these algorithms is measured using simulations. This paper also attempts to derandomize the randomized online algorithm for this problem

Cell-Free Massive MIMO versus Small Cells

A Cell-Free Massive MIMO (multiple-input multiple-output) system comprises a very large number of distributed access points (APs)which simultaneously serve a much smaller number of users over the same time/frequency resources based on directly measured channel characteristics. The APs and users have only one antenna each. The APs acquire channel state information through time-division duplex operation and the reception of uplink pilot signals transmitted by the users. The APs perform multiplexing/de-multiplexing through conjugate beamforming on the downlink and matched filtering on the uplink. Closed-form expressions for individual user uplink and downlink throughputs lead to max-min power control algorithms. Max-min power control ensures uniformly good service throughout the area of coverage. A pilot assignment algorithm helps to mitigate the effects of pilot contamination, but power control is far more important in that regard. Cell-Free Massive MIMO has considerably improved performance with respect to a conventional small-cell scheme, whereby each user is served by a dedicated AP, in terms of both 95%-likely per-user throughput and immunity to shadow fading spatial correlation. Under uncorrelated shadow fading conditions, the cell-free scheme provides nearly 5-fold improvement in 95%-likely per-user throughput over the small-cell scheme, and 10-fold improvement when shadow fading is correlated.Comment: EEE Transactions on Wireless Communications, accepted for publicatio

Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model

We consider online scheduling on multiple machines for jobs arriving one-by-one with the objective of minimizing the makespan. For any number of identical parallel or uniformly related machines, we provide a competitive-ratio approximation scheme that computes an online algorithm whose competitive ratio is arbitrarily close to the best possible competitive ratio. We also determine this value up to any desired accuracy. This is the first application of competitive-ratio approximation schemes in the online-list model. The result proves the applicability of the concept in different online models. We expect that it fosters further research on other online problems