The Role of Inter-Controller Traffic for Placement of Distributed SDN Controllers

We consider a distributed Software Defined Networking (SDN) architecture adopting a cluster of multiple controllers to improve network performance and reliability. Besides the Openflow control traffic exchanged between controllers and switches, we focus on the control traffic exchanged among the controllers in the cluster, needed to run coordination and consensus algorithms to keep the controllers synchronized. We estimate the effect of the inter-controller communications on the reaction time perceived by the switches depending on the data-ownership model adopted in the cluster. The model is accurately validated in an operational Software Defined WAN (SDWAN). We advocate a careful placement of the controllers, that should take into account both the above kinds of control traffic. We evaluate, for some real ISP network topologies, the delay tradeoffs for the controllers placement problem and we propose a novel evolutionary algorithm to find the corresponding Pareto frontier. Our work provides novel quantitative tools to optimize the planning and the design of the network supporting the control plane of SDN networks, especially when the network is very large and in-band control plane is adopted. We also show that for operational distributed controllers (e.g. OpenDaylight and ONOS), the location of the controller which acts as a leader in the consensus algorithm has a strong impact on the reactivity perceived by switches.Comment: 14 page

Deterministic Time-Space Tradeoffs for k-SUM

Given a set of numbers, the $k$-SUM problem asks for a subset of $k$ numbers that sums to zero. When the numbers are integers, the time and space complexity of $k$-SUM is generally studied in the word-RAM model; when the numbers are reals, the complexity is studied in the real-RAM model, and space is measured by the number of reals held in memory at any point. We present a time and space efficient deterministic self-reduction for the $k$-SUM problem which holds for both models, and has many interesting consequences. To illustrate: * $3$-SUM is in deterministic time $O(n^2 \lg\lg(n)/\lg(n))$ and space $O\left(\sqrt{\frac{n \lg(n)}{\lg\lg(n)}}\right)$. In general, any polylogarithmic-time improvement over quadratic time for $3$-SUM can be converted into an algorithm with an identical time improvement but low space complexity as well. * $3$-SUM is in deterministic time $O(n^2)$ and space $O(\sqrt n)$, derandomizing an algorithm of Wang. * A popular conjecture states that 3-SUM requires $n^{2-o(1)}$ time on the word-RAM. We show that the 3-SUM Conjecture is in fact equivalent to the (seemingly weaker) conjecture that every $O(n^{.51})$-space algorithm for $3$-SUM requires at least $n^{2-o(1)}$ time on the word-RAM. * For $k \ge 4$, $k$-SUM is in deterministic $O(n^{k - 2 + 2/k})$ time and $O(\sqrt{n})$ space

Using Hashing to Solve the Dictionary Problem (In External Memory)

We consider the dictionary problem in external memory and improve the update time of the well-known buffer tree by roughly a logarithmic factor. For any \lambda >= max {lg lg n, log_{M/B} (n/B)}, we can support updates in time O(\lambda / B) and queries in sublogarithmic time, O(log_\lambda n). We also present a lower bound in the cell-probe model showing that our data structure is optimal. In the RAM, hash tables have been used to solve the dictionary problem faster than binary search for more than half a century. By contrast, our data structure is the first to beat the comparison barrier in external memory. Ours is also the first data structure to depart convincingly from the indivisibility paradigm

Complex Block Floating-Point Format with Box Encoding For Wordlength Reduction in Communication Systems

We propose a new complex block floating-point format to reduce implementation complexity. The new format achieves wordlength reduction by sharing an exponent across the block of samples, and uses box encoding for the shared exponent to reduce quantization error. Arithmetic operations are performed on blocks of samples at time, which can also reduce implementation complexity. For a case study of a baseband quadrature amplitude modulation (QAM) transmitter and receiver, we quantify the tradeoffs in signal quality vs. implementation complexity using the new approach to represent IQ samples. Signal quality is measured using error vector magnitude (EVM) in the receiver, and implementation complexity is measured in terms of arithmetic complexity as well as memory allocation and memory input/output rates. The primary contributions of this paper are (1) a complex block floating-point format with box encoding of the shared exponent to reduce quantization error, (2) arithmetic operations using the new complex block floating-point format, and (3) a QAM transceiver case study to quantify signal quality vs. implementation complexity tradeoffs using the new format and arithmetic operations.Comment: 6 pages, 9 figures, submitted to Asilomar Conference on Signals, Systems, and Computers 201

Progress-Space Tradeoffs in Single-Writer Memory Implementations

Many algorithms designed for shared-memory distributed systems assume the single-writer multi- reader (SWMR) setting where each process is provided with a unique register that can only be written by the process and read by all. In a system where computation is performed by a bounded number n of processes coming from a large (possibly unbounded) set of potential participants, the assumption of an SWMR memory is no longer reasonable. If only a bounded number of multi- writer multi-reader (MWMR) registers are provided, we cannot rely on an a priori assignment of processes to registers. In this setting, implementing an SWMR memory, or equivalently, ensuring stable writes (i.e., every written value persists in the memory), is desirable. In this paper, we propose an SWMR implementation that adapts the number of MWMR registers used to the desired progress condition. For any given k from 1 to n, we present an algorithm that uses n + k ? 1 registers to implement a k-lock-free SWMR memory. In the special case of 2-lock-freedom, we also give a matching lower bound of n + 1 registers, which supports our conjecture that the algorithm is space-optimal. Our lower bound holds for the strictly weaker progress condition of 2-obstruction-freedom, which suggests that the space complexity for k-obstruction-free and k-lock-free SWMR implementations might coincide

Middleware-based Database Replication: The Gaps between Theory and Practice

The need for high availability and performance in data management systems has been fueling a long running interest in database replication from both academia and industry. However, academic groups often attack replication problems in isolation, overlooking the need for completeness in their solutions, while commercial teams take a holistic approach that often misses opportunities for fundamental innovation. This has created over time a gap between academic research and industrial practice. This paper aims to characterize the gap along three axes: performance, availability, and administration. We build on our own experience developing and deploying replication systems in commercial and academic settings, as well as on a large body of prior related work. We sift through representative examples from the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies from real systems deployed at Fortune 500 customers. We propose two agendas, one for academic research and one for industrial R&D, which we believe can bridge the gap within 5-10 years. This way, we hope to both motivate and help researchers in making the theory and practice of middleware-based database replication more relevant to each other.Comment: 14 pages. Appears in Proc. ACM SIGMOD International Conference on Management of Data, Vancouver, Canada, June 200

CATS: linearizability and partition tolerance in scalable and self-organizing key-value stores

Distributed key-value stores provide scalable, fault-tolerant, and self-organizing storage services, but fall short of guaranteeing linearizable consistency in partially synchronous, lossy, partitionable, and dynamic networks, when data is distributed and replicated automatically by the principle of consistent hashing. This paper introduces consistent quorums as a solution for achieving atomic consistency. We present the design and implementation of CATS, a distributed key-value store which uses consistent quorums to guarantee linearizability and partition tolerance in such adverse and dynamic network conditions. CATS is scalable, elastic, and self-organizing; key properties for modern cloud storage middleware. Our system shows that consistency can be achieved with practical performance and modest throughput overhead (5%) for read-intensive workloads

Early Quantitative Assessment of Non-Functional Requirements

Non-functional requirements (NFRs) of software systems are a well known source of uncertainty in effort estimation. Yet, quantitatively approaching NFR early in a project is hard. This paper makes a step towards reducing the impact of uncertainty due to NRF. It offers a solution that incorporates NFRs into the functional size quantification process. The merits of our solution are twofold: first, it lets us quantitatively assess the NFR modeling process early in the project, and second, it lets us generate test cases for NFR verification purposes. We chose the NFR framework as a vehicle to integrate NFRs into the requirements modeling process and to apply quantitative assessment procedures. Our solution proposal also rests on the functional size measurement method, COSMIC-FFP, adopted in 2003 as the ISO/IEC 19761 standard. We extend its use for NFR testing purposes, which is an essential step for improving NFR development and testing effort estimates, and consequently for managing the scope of NFRs. We discuss the advantages of our approach and the open questions related to its design as well

A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs

We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct product theorem for 2-sided error quantum algorithms computing k independent instances of a symmetric Boolean function: if the algorithm uses significantly less than k times the number of queries needed for one instance of the function, then its success probability is exponentially small in k. We also use the polynomial method to prove a direct product theorem for 1-sided error algorithms for k threshold functions with a stronger bound on the success probability. Finally, we present a quantum algorithm for evaluating solutions to systems of linear inequalities, and use our direct product theorems to show that the time-space tradeoff of this algorithm is close to optimal.Comment: 16 pages LaTeX. Version 2: title changed, proofs significantly cleaned up and made selfcontained. This version to appear in the proceedings of the STOC 06 conferenc