Precedence-Constrained Min Sum Set Cover

We introduce a version of the Min Sum Set Cover (MSSC) problem in which there are "AND" precedence constraints on the m sets. In the Precedence-Constrained Min Sum Set Cover (PCMSSC) problem, when interpreted as directed edges, the constraints induce an acyclic directed graph. PCMSSC models the aim of scheduling software tests to prioritize the rate of fault detection subject to dependencies between tests. Our greedy scheme for PCMSSC is similar to the approaches of Feige, Lovasz, and, Tetali for MSSC, and Chekuri and Motwani for precedence-constrained scheduling to minimize weighted completion time. With a factor-4 increase in approximation ratio, we reduce PCMSSC to the problem of finding a maximum-density precedence-closed sub-family of sets, where density is the ratio of sub-family union size to cardinality. We provide a greedy factor-sqrt m algorithm for maximizing density; on forests of in-trees, we show this algorithm finds an optimal solution. Harnessing an alternative greedy argument of Chekuri and Kumar for Maximum Coverage with Group Budget Constraints, on forests of out-trees, we design an algorithm with approximation ratio equal to maximum tree height. Finally, with a reduction from the Planted Dense Subgraph detection problem, we show that its conjectured hardness implies there is no polynomial-time algorithm for PCMSSC with approximation factor in O(m^{1/12-epsilon})

Optimal control of hepatitis C antiviral treatment programme delivery for prevention amongst a population of injecting drug users.

In most developed countries, HCV is primarily transmitted by injecting drug users (IDUs). HCV antiviral treatment is effective, and deemed cost-effective for those with no re-infection risk. However, few active IDUs are currently treated. Previous modelling studies have shown antiviral treatment for active IDUs could reduce HCV prevalence, and there is emerging interest in developing targeted IDU treatment programmes. However, the optimal timing and scale-up of treatment is unknown, given the real-world constraints commonly existing for health programmes. We explore how the optimal programme is affected by a variety of policy objectives, budget constraints, and prevalence settings. We develop a model of HCV transmission and treatment amongst active IDUs, determine the optimal treatment programme strategy over 10 years for two baseline chronic HCV prevalence scenarios (30% and 45%), a range of maximum annual budgets (£50,000-300,000 per 1,000 IDUs), and a variety of objectives: minimising health service costs and health utility losses; minimising prevalence at 10 years; minimising health service costs and health utility losses with a final time prevalence target; minimising health service costs with a final time prevalence target but neglecting health utility losses. The largest programme allowed for a given budget is the programme which minimises both prevalence at 10 years, and HCV health utility loss and heath service costs, with higher budgets resulting in greater cost-effectiveness (measured by cost per QALY gained compared to no treatment). However, if the objective is to achieve a 20% relative prevalence reduction at 10 years, while minimising both health service costs and losses in health utility, the optimal treatment strategy is an immediate expansion of coverage over 5-8 years, and is less cost-effective. By contrast, if the objective is only to minimise costs to the health service while attaining the 20% prevalence reduction, the programme is deferred until the final years of the decade, and is the least cost-effective of the scenarios

Frame Based Precoding in Satellite Communications: A Multicast Approach

In the present work, a multibeam satellite that employs aggressive frequency reuse towards increasing the offered throughput is considered. Focusing on the forward link, the goal is to employ multi-antenna signal processing techniques, namely linear precoding, to manage the inter-beam interferences. In this context, fundamental practical limitations, namely the rigid framing structure of satellite communication standards and the on-board per-antenna power constraints, are herein considered. Therefore, the concept of optimal frame based precoding under per-antenna constraints, is discussed. This consists in precoding the transmit signals without changing the underlying framing structure of the communication standard. In the present work, the connection of the frame based precoding problem with the generic signal processing problem of conveying independent sets of common data to distinct groups of users is established. This model is known as physical layer multicasting to multiple co-channel groups. Building on recent results, the weighted fair per-antenna power constrained multigroup multicast precoders are employed for frame based precoding. The throughput performance of these solutions is compared to multicast aware heuristic precoding methods over a realistic multibeam satellite scenario. Consequently, the gains of the proposed approach are quantified via extensive numerical results.Comment: Accepted for presentation at the IEEE ASMS 201