Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo

Distributed Algorithms for Scheduling on Line and Tree Networks

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $$, along with a profit; the processor wishes to send data between $u$ and $v$. Towards that goal, the processor needs to select a graph network accessible to it and a path connecting $u$ and $v$ within the selected network. The processor requires exclusive access to the chosen path, in order to route the data. Thus, the processors are competing for routes/channels. A feasible solution selects a subset of demands and schedules each selected demand on a graph network accessible to the processor owning the demand; the solution also specifies the paths to use for this purpose. The requirement is that for any two demands scheduled on the same graph network, their chosen paths must be edge disjoint. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distibuted setting for the special case where all the graph networks are simply paths (i.e, line-networks). Distributed constant factor approximation algorithms are known for this case. The main contributions of this paper are twofold. First we design a distributed constant factor approximation algorithm for the more general case of tree-networks. The core component of our algorithm is a tree-decomposition technique, which may be of independent interest. Secondly, for the case of line-networks, we improve the known approximation guarantees by a factor of 5. Our algorithms can also handle the capacitated scenario, wherein the demands and edges have bandwidth requirements and capacities, respectively.Comment: Accepted to PODC 2012, full versio

A Near-linear Time Constant Factor Algorithm for Unsplittable Flow Problem on Line with Bag Constraints

Consider a scenario where we need to schedule a set of jobs on a system offering some resource (such as electrical power or communication bandwidth), which we shall refer to as bandwidth. Each job consists of a set (or bag) of job instances. For each job instance, the input specifies the start time, finish time, bandwidth requirement and profit. The bandwidth offered by the system varies at different points of time and is specified as part of the input. A feasible solution is to choose a subset of instances such that at any point of time, the sum of bandwidth requirements of the chosen instances does not exceed the bandwidth available at that point of time, and furthermore, at most one instance is picked from each job. The goal is to find a maximum profit feasible solution. We study this problem under a natural assumption called the no-bottleneck assumption (NBA), wherein the bandwidth requirement of any job instance is at most the minimum bandwidth available. We present a simple, near-linear time constant factor approximation algorithm for this problem, under NBA. When each job consists of only one job instance, the above problem is the same as the well-studied unsplittable flow problem (UFP) on lines. A constant factor approximation algorithm is known for the UFP on line, under NBA. Our result leads to an alternative constant factor approximation algorithm for this problem. Though the approximation ratio achieved by our algorithm is inferior, it is much simpler, deterministic and faster in comparison to the existing algorithms. Our algorithm runs in near-linear time ($O(n*log^2 n)$), whereas the running time of the known algorithms is a high order polynomial. The core idea behind our algorithm is a reduction from the varying bandwidth case to the easier uniform bandwidth case, using a technique that we call slicing

Dynamic Time-domain Duplexing for Self-backhauled Millimeter Wave Cellular Networks

Millimeter wave (mmW) bands between 30 and 300 GHz have attracted considerable attention for next-generation cellular networks due to vast quantities of available spectrum and the possibility of very high-dimensional antenna ar-rays. However, a key issue in these systems is range: mmW signals are extremely vulnerable to shadowing and poor high-frequency propagation. Multi-hop relaying is therefore a natural technology for such systems to improve cell range and cell edge rates without the addition of wired access points. This paper studies the problem of scheduling for a simple infrastructure cellular relay system where communication between wired base stations and User Equipment follow a hierarchical tree structure through fixed relay nodes. Such a systems builds naturally on existing cellular mmW backhaul by adding mmW in the access links. A key feature of the proposed system is that TDD duplexing selections can be made on a link-by-link basis due to directional isolation from other links. We devise an efficient, greedy algorithm for centralized scheduling that maximizes network utility by jointly optimizing the duplexing schedule and resources allocation for dense, relay-enhanced OFDMA/TDD mmW networks. The proposed algorithm can dynamically adapt to loading, channel conditions and traffic demands. Significant throughput gains and improved resource utilization offered by our algorithm over the static, globally-synchronized TDD patterns are demonstrated through simulations based on empirically-derived channel models at 28 GHz.Comment: IEEE Workshop on Next Generation Backhaul/Fronthaul Networks - BackNets 201

A note on the data-driven capacity of P2P networks

We consider two capacity problems in P2P networks. In the first one, the nodes have an infinite amount of data to send and the goal is to optimally allocate their uplink bandwidths such that the demands of every peer in terms of receiving data rate are met. We solve this problem through a mapping from a node-weighted graph featuring two labels per node to a max flow problem on an edge-weighted bipartite graph. In the second problem under consideration, the resource allocation is driven by the availability of the data resource that the peers are interested in sharing. That is a node cannot allocate its uplink resources unless it has data to transmit first. The problem of uplink bandwidth allocation is then equivalent to constructing a set of directed trees in the overlay such that the number of nodes receiving the data is maximized while the uplink capacities of the peers are not exceeded. We show that the problem is NP-complete, and provide a linear programming decomposition decoupling it into a master problem and multiple slave subproblems that can be resolved in polynomial time. We also design a heuristic algorithm in order to compute a suboptimal solution in a reasonable time. This algorithm requires only a local knowledge from nodes, so it should support distributed implementations. We analyze both problems through a series of simulation experiments featuring different network sizes and network densities. On large networks, we compare our heuristic and its variants with a genetic algorithm and show that our heuristic computes the better resource allocation. On smaller networks, we contrast these performances to that of the exact algorithm and show that resource allocation fulfilling a large part of the peer can be found, even for hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio

Embedding of Virtual Network Requests over Static Wireless Multihop Networks

Network virtualization is a technology of running multiple heterogeneous network architecture on a shared substrate network. One of the crucial components in network virtualization is virtual network embedding, which provides a way to allocate physical network resources (CPU and link bandwidth) to virtual network requests. Despite significant research efforts on virtual network embedding in wired and cellular networks, little attention has been paid to that in wireless multi-hop networks, which is becoming more important due to its rapid growth and the need to share these networks among different business sectors and users. In this paper, we first study the root causes of new challenges of virtual network embedding in wireless multi-hop networks, and propose a new embedding algorithm that efficiently uses the resources of the physical substrate network. We examine our algorithm's performance through extensive simulations under various scenarios. Due to lack of competitive algorithms, we compare the proposed algorithm to five other algorithms, mainly borrowed from wired embedding or artificially made by us, partially with or without the key algorithmic ideas to assess their impacts.Comment: 22 page

An Innovative RAN Architecture for Emerging Heterogeneous Networks: The Road to the 5G Era

The global demand for mobile-broadband data services has experienced phenomenal growth over the last few years, driven by the rapid proliferation of smart devices such as smartphones and tablets. This growth is expected to continue unabated as mobile data traffic is predicted to grow anywhere from 20 to 50 times over the next 5 years. Exacerbating the problem is that such unprecedented surge in smartphones usage, which is characterized by frequent short on/off connections and mobility, generates heavy signaling traffic load in the network signaling storms . This consumes a disproportion amount of network resources, compromising network throughput and efficiency, and in extreme cases can cause the Third-Generation (3G) or 4G (long-term evolution (LTE) and LTE-Advanced (LTE-A)) cellular networks to crash. As the conventional approaches of improving the spectral efficiency and/or allocation additional spectrum are fast approaching their theoretical limits, there is a growing consensus that current 3G and 4G (LTE/LTE-A) cellular radio access technologies (RATs) won\u27t be able to meet the anticipated growth in mobile traffic demand. To address these challenges, the wireless industry and standardization bodies have initiated a roadmap for transition from 4G to 5G cellular technology with a key objective to increase capacity by 1000Ã? by 2020 . Even though the technology hasn\u27t been invented yet, the hype around 5G networks has begun to bubble. The emerging consensus is that 5G is not a single technology, but rather a synergistic collection of interworking technical innovations and solutions that collectively address the challenge of traffic growth. The core emerging ingredients that are widely considered the key enabling technologies to realize the envisioned 5G era, listed in the order of importance, are: 1) Heterogeneous networks (HetNets); 2) flexible backhauling; 3) efficient traffic offload techniques; and 4) Self Organizing Networks (SONs). The anticipated solutions delivered by efficient interworking/ integration of these enabling technologies are not simply about throwing more resources and /or spectrum at the challenge. The envisioned solution, however, requires radically different cellular RAN and mobile core architectures that efficiently and cost-effectively deploy and manage radio resources as well as offload mobile traffic from the overloaded core network. The main objective of this thesis is to address the key techno-economics challenges facing the transition from current Fourth-Generation (4G) cellular technology to the 5G era in the context of proposing a novel high-risk revolutionary direction to the design and implementation of the envisioned 5G cellular networks. The ultimate goal is to explore the potential and viability of cost-effectively implementing the 1000x capacity challenge while continuing to provide adequate mobile broadband experience to users. Specifically, this work proposes and devises a novel PON-based HetNet mobile backhaul RAN architecture that: 1) holistically addresses the key techno-economics hurdles facing the implementation of the envisioned 5G cellular technology, specifically, the backhauling and signaling challenges; and 2) enables, for the first time to the best of our knowledge, the support of efficient ground-breaking mobile data and signaling offload techniques, which significantly enhance the performance of both the HetNet-based RAN and LTE-A\u27s core network (Evolved Packet Core (EPC) per 3GPP standard), ensure that core network equipment is used more productively, and moderate the evolving 5G\u27s signaling growth and optimize its impact. To address the backhauling challenge, we propose a cost-effective fiber-based small cell backhaul infrastructure, which leverages existing fibered and powered facilities associated with a PON-based fiber-to-the-Node/Home (FTTN/FTTH)) residential access network. Due to the sharing of existing valuable fiber assets, the proposed PON-based backhaul architecture, in which the small cells are collocated with existing FTTN remote terminals (optical network units (ONUs)), is much more economical than conventional point-to-point (PTP) fiber backhaul designs. A fully distributed ring-based EPON architecture is utilized here as the fiber-based HetNet backhaul. The techno-economics merits of utilizing the proposed PON-based FTTx access HetNet RAN architecture versus that of traditional 4G LTE-A\u27s RAN will be thoroughly examined and quantified. Specifically, we quantify the techno-economics merits of the proposed PON-based HetNet backhaul by comparing its performance versus that of a conventional fiber-based PTP backhaul architecture as a benchmark. It is shown that the purposely selected ring-based PON architecture along with the supporting distributed control plane enable the proposed PON-based FTTx RAN architecture to support several key salient networking features that collectively significantly enhance the overall performance of both the HetNet-based RAN and 4G LTE-A\u27s core (EPC) compared to that of the typical fiber-based PTP backhaul architecture in terms of handoff capability, signaling overhead, overall network throughput and latency, and QoS support. It will also been shown that the proposed HetNet-based RAN architecture is not only capable of providing the typical macro-cell offloading gain (RAN gain) but also can provide ground-breaking EPC offloading gain. The simulation results indicate that the overall capacity of the proposed HetNet scales with the number of deployed small cells, thanks to LTE-A\u27s advanced interference management techniques. For example, if there are 10 deployed outdoor small cells for every macrocell in the network, then the overall capacity will be approximately 10-11x capacity gain over a macro-only network. To reach the 1000x capacity goal, numerous small cells including 3G, 4G, and WiFi (femtos, picos, metros, relays, remote radio heads, distributed antenna systems) need to be deployed indoors and outdoors, at all possible venues (residences and enterprises)