From Electrical Power Flows to Unsplittabe Flows: A QPTAS for OPF with Discrete Demands in Line Distribution Networks

The {\it AC Optimal Power Flow} (OPF) problem is a fundamental problem in power systems engineering which has been known for decades. It is a notoriously hard problem due mainly to two reasons: (1) non-convexity of the power flow constraints and (2) the (possible) existence of discrete power injection constraints. Recently, sufficient conditions were provided for certain convex relaxations of OPF to be exact in the continuous case, thus allowing one to partially address the issue of non-convexity. In this paper we make a first step towards addressing the combinatorial issue. Namely, by establishing a connection to the well-known {\it unsplittable flow problem} (UFP), we are able to generalize known techniques for the latter problem to provide approximation algorithms for OPF with discrete demands. As an application, we give a quasi-polynomial time approximation scheme for OPF in line networks under some mild assumptions and a single generation source. We believe that this connection can be further leveraged to obtain approximation algorithms for more general settings, such as multiple generation sources and tree networks

Content Placement as a Key to a Content-Dominated, Highly mobile Internet

Most of the Internet traffic is content, and most of the Internet connected hosts are mobile. Our work focuses on the design of infrastructure services needed to support such a content-dominated, highly mobile Internet. In the design of these services, three sets of decisions arise frequently: (1) Content placment for selecting the locations where a content is placed, (2) request redirection for selecting the location where a particular request is served from and (3) network routing for selecting the physical path between clients and the services they are accessing. Our central thesis is that content placement is a powerful factor, and is often more powerful than redirection and routing, in determining the cost, performance and energy-related metrics for these services. In support of this thesis, we consider three types of infrastructure. Internet service provider (ISP): In an ISP carrying content-dominated traffic, we show that combinations of simple placement and routing schemes are effective in optimizing an ISP\u27s performance and cost objectives. Further, we show that effective content placement contributes more than optimizing network routing to achieve an ISP\u27s objectives. Our findings question the value of traditional ISP traffic engineering schemes that optimize routing alone, while simplifying the task of traffic engineering for the operators. Global name service (GNS): We design and implement a GNS, \auspice, that resolves names to network addresses for highly mobile entities, thereby providing a key building block for establishing communication between mobile entities in the Internet. A key distinction between \auspice\ and other name services is a {\em demand-aware} replica {placement engine} that intelligently replicates name records to provide low lookup latency, low update cost, and high availability. In our experiments, Auspice\u27s placement scheme enables it to significantly outperform commercial managed DNS providers, DHT-based replication as well as static placement schemes that use the same redirection scheme as Auspice. Content datacenter (CDC): Content datacenters cache and serve content to improve user-perceived performance for content accesses. In a CDC, we quantify the tradeoff between energy savings via consolidation and the user-perceived performance impact based on a real CDC workload. A key insight, supported via experiments, is that despite server consolidation, a simple caching scheme is able to achieve cache hit rates close to an unconsolidated datacenter, which helps mitigate the impact of consolidation on user-perceived latencies. Further, our work is the first to propose a network-aware server consolidation approach that enables additional network energy savings over network-unaware server consolidation schemes for common datacenter topologies

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum