arXiv subjects

SunYoung Kim

Publications and source records attributed to SunYoung Kim.

4 recordsLinked to original sources

arXiv2021

Count-Less: A Counting Sketch for the Data Plane of High Speed Switches

Demands are increasing to measure per-flow statistics in the data plane of high-speed switches. Measuring flows with exact counting is infeasible due to processing and memory constraints, but a sketch is a promising candidate for collecting approximately per-flow statistics in data plane in real-time. Among them, Count-Min sketch is a versatile tool to measure spectral density of high volume data using a small amount of memory and low processing overhead. Due to its simplicity and versatility, Count-Min sketch and its variants have been adopted in many works as a stand alone or even as a supporting measurement tool. However, Count-Min's estimation accuracy is limited owing to its data structure not fully accommodating Zipfian distribution and the indiscriminate update algorithm without considering a counter value. This in turn degrades the accuracy of heavy hitter, heavy changer, cardinality, and entropy. To enhance measurement accuracy of Count-Min, there have been many and various attempts. One of the most notable approaches is to cascade multiple sketches in a sequential manner so that either mouse or elephant flows should be filtered to separate elephants from mouse flows such as Elastic sketch (an elephant filter leveraging TCAM + Count-Min) and FCM sketch (Count-Min-based layered mouse filters). In this paper, we first show that these cascaded filtering approaches adopting a Pyramid-shaped data structure (allocating more counters for mouse flows) still suffer from under-utilization of memory, which gives us a room for better estimation. To this end, we are facing two challenges: one is (a) how to make Count-Min's data structure accommodate more effectively Zipfian distribution, and the other is (b) how to make update and query work without delaying packet processing in the switch's data plane. Count-Less adopts a different combination ...

cs.NI↗

arXiv2016

Semantics, Specification Logic, and Hoare Logic of Exact Real Computation

We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture multi-valuedness, which is well-known to be essential to real number computation, we use a Plotkin powerdomain and make our programming language semantics computable and complete: all and only real functions computable in computable analysis can be realized in ERC. The base programming language supports real arithmetic as well as implicit limits; expansions support additional primitive operations (such as a user-defined exponential function). By restricting integers to Presburger arithmetic and real coercion to the `precision' embedding $\mathbb{Z}\ni p\mapsto 2^p\in\mathbb{R}$, we arrive at a first-order theory which we prove to be decidable and model-complete. Based on said logic as specification language for preconditions and postconditions, we extend Hoare logic to a sound (w.r.t. the denotational semantics) and expressive system for deriving correct total correctness specifications. Various examples demonstrate the practicality and convenience of our language and the extended Hoare logic.

math.NA↗

arXiv2015

Non-commutative groupoids obtained from the failure of $3$-uniqueness in stable theories

We construct a possibly non-commutative groupoid from the failure of $3$-uniqueness of a strong type. The commutative groupoid constructed by John Goodrick and Alexei Kolesnikov in \cite{GK} lives in the center of the groupoid. A certain automorphism group approximated by the vertex groups of the non-commutative groupoids is suggested as a "fundamental group" of the strong type.

math.LO↗

arXiv2015

A classification of 2-chains having 1-shell boundaries in rosy theories

We classify, in a non-trivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial. We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal lengths of $2$-chains whose boundary is a $1$-shell.

math.LO↗