Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Our second algorithm handles an arbitrary sequence of arc additions in $O(n^{5/2})$ time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take $\Omega(n^2 2^{\sqrt{2\lg n}})$ time by relating its performance to a generalization of the $k$-levels problem of combinatorial geometry. A completely different algorithm running in $\Theta(n^2 \log n)$ time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.Comment: 31 page

Datacenter Traffic Control: Understanding Techniques and Trade-offs

Datacenters provide cost-effective and flexible access to scalable compute and storage resources necessary for today's cloud computing needs. A typical datacenter is made up of thousands of servers connected with a large network and usually managed by one operator. To provide quality access to the variety of applications and services hosted on datacenters and maximize performance, it deems necessary to use datacenter networks effectively and efficiently. Datacenter traffic is often a mix of several classes with different priorities and requirements. This includes user-generated interactive traffic, traffic with deadlines, and long-running traffic. To this end, custom transport protocols and traffic management techniques have been developed to improve datacenter network performance. In this tutorial paper, we review the general architecture of datacenter networks, various topologies proposed for them, their traffic properties, general traffic control challenges in datacenters and general traffic control objectives. The purpose of this paper is to bring out the important characteristics of traffic control in datacenters and not to survey all existing solutions (as it is virtually impossible due to massive body of existing research). We hope to provide readers with a wide range of options and factors while considering a variety of traffic control mechanisms. We discuss various characteristics of datacenter traffic control including management schemes, transmission control, traffic shaping, prioritization, load balancing, multipathing, and traffic scheduling. Next, we point to several open challenges as well as new and interesting networking paradigms. At the end of this paper, we briefly review inter-datacenter networks that connect geographically dispersed datacenters which have been receiving increasing attention recently and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial

Combining request scheduling with web caching

We extend the classic paging model by allowing reordering of requests under the constraint that a request is delayed by no longer than a predetermined number of time steps. We first give a dynamic programming algorithm to solve the offline case. Then we give tight bounds on competitive ratios for the online case. For caches of size k, we obtain bounds of k + O(1) for deterministic algorithms and Theta(log k) for randomized algorithms. We also give bounds for the case where either the online or the offline algorithm can reorder the requests, but not both. Finally, we extend our analysis to the case where pages have different sizes

Endpoint-transparent Multipath Transport with Software-defined Networks

Multipath forwarding consists of using multiple paths simultaneously to transport data over the network. While most such techniques require endpoint modifications, we investigate how multipath forwarding can be done inside the network, transparently to endpoint hosts. With such a network-centric approach, packet reordering becomes a critical issue as it may cause critical performance degradation. We present a Software Defined Network architecture which automatically sets up multipath forwarding, including solutions for reordering and performance improvement, both at the sending side through multipath scheduling algorithms, and the receiver side, by resequencing out-of-order packets in a dedicated in-network buffer. We implemented a prototype with commonly available technology and evaluated it in both emulated and real networks. Our results show consistent throughput improvements, thanks to the use of aggregated path capacity. We give comparisons to Multipath TCP, where we show our approach can achieve a similar performance while offering the advantage of endpoint transparency