Biblio

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems: in some cases, a big graph is chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to certain suboptimality from the interaction among different pieces. In other cases, links between different parts may show up in the running time and/or network communications cost, hence the desire to have small cut size. We study a distributed balanced partitioning problem where the goal is to partition the vertices of a given graph into k pieces, minimizing the total cut size. Our algorithm is composed of a few steps that are easily implementable in distributed computation frameworks, e.g., MapReduce. The algorithm first embeds nodes of the graph onto a line, and then processes nodes in a distributed manner guided by the linear embedding order. We examine various ways to find the first embedding, e.g., via a hierarchical clustering or Hilbert curves. Then we apply four different techniques such as local swaps, minimum cuts on partition boundaries, as well as contraction and dynamic programming. Our empirical study compares the above techniques with each other, and to previous work in distributed algorithms, e.g., a label propagation method, FENNEL and Spinner. We report our results both on a private map graph and several public social networks, and show that our results beat previous distributed algorithms: we notice, e.g., 15-25% reduction in cut size over [UB13]. We also observe that our algorithms allow for scalable distributed implementation for any number of partitions. Finally, we apply our techniques for the Google Maps Driving Directions to minimize the number of multi-shard queries with the goal of saving in CPU usage. During live experiments, we observe an ≈ 40% drop in the number of multi-shard queries when comparing our method with a standard geography-based method.

Reactive synthesis with the ambitious goal of automatically synthesizing correct-by-construction controllers from high-level specifications, has recently attracted significant attention in system design and control. In practice, complex systems are often not constructed from scratch but from a set of existing building blocks. For example in robot motion planning, a robot usually has a number of predefined motion primitives that can be selected and composed to enforce a high-level objective. In this paper, we propose a novel framework for synthesis from a library of parametric and reactive controllers. Parameters allow us to take advantage of the symmetry in many synthesis problems. Reactivity of the controllers takes into account that the environment may be dynamic and potentially adversarial. We first show how these controllers can be automatically constructed from parametric objectives specified by the user to form a library of parametric and reactive controllers. We then give a synthesis algorithm that selects and instantiates controllers from the library in order to satisfy a given linear temporal logic objective. We implement our algorithms symbolically and illustrate the potential of our method by applying it to an autonomous vehicle case study.

Modern shared memory multiprocessors permit reordering of memory operations for performance reasons. These reorderings are often a source of subtle bugs in programs written for such architectures. Traditional approaches to verify weak memory programs often rely on interleaving semantics, which is prone to state space explosion, and thus severely limits the scalability of the analysis. In recent times, there has been a renewed interest in modelling dynamic executions of weak memory programs using partial orders. However, such an approach typically requires ad-hoc mechanisms to correctly capture the data and control-flow choices/conflicts present in real-world programs. In this work, we propose a novel, conflict-aware, composable, truly concurrent semantics for programs written using C/C++ for modern weak memory architectures. We exploit our symbolic semantics based on general event structures to build an efficient decision procedure that detects assertion violations in bounded multi-threaded programs. Using a large, representative set of benchmarks, we show that our conflict-aware semantics outperforms the state-of-the-art partial-order based approaches.

This work describes the design, implementation, and evaluation of Λολ, a general-purpose software framework for lattice-based cryptography. The Λολ framework has several novel properties that distinguish it from prior implementations of lattice cryptosystems, including the following. Generality, modularity, concision: Λολ defines a collection of general, highly composable interfaces for mathematical operations used across lattice cryptography, allowing for a wide variety of schemes to be expressed very naturally and at a high level of abstraction. For example, we implement an advanced fully homomorphic encryption (FHE) scheme in as few as 2–5 lines of code per feature, via code that very closely matches the scheme's mathematical definition. Theory affinity: Λολ is designed from the ground-up around the specialized ring representations, fast algorithms, and worst-case hardness proofs that have been developed for the Ring-LWE problem and its cryptographic applications. In particular, it implements fast algorithms for sampling from theory-recommended error distributions over arbitrary cyclotomic rings, and provides tools for maintaining tight control of error growth in cryptographic schemes. Safety: Λολ has several facilities for reducing code complexity and programming errors, thereby aiding the correct implementation of lattice cryptosystems. In particular, it uses strong typing to statically enforce—i.e., at compile time—a wide variety of constraints among the various parameters. Advanced features: Λολ exposes the rich hierarchy of cyclotomic rings to cryptographic applications. We use this to give the first-ever implementation of a collection of FHE operations known as "ring switching," and also define and analyze a more efficient variant that we call "ring tunneling." Lastly, this work defines and analyzes a variety of mathematical objects and algorithms for the recommended usage of Ring-LWE in cyclotomic rings, which we believe will serve as a useful knowledge base for future implementations.

Today’s Internet services are often expected to stay available and render high responsiveness even in the face of site crashes and network partitions. Theoretical results state that causal consistency is one of the strongest consistency guarantees that is possible under these requirements, and many practical systems provide causally consistent key-value stores. In this paper, we present a framework called Chapar for modular verification of causal consistency for replicated key-value store implementations and their client programs. Specifically, we formulate separate correctness conditions for key-value store implementations and for their clients. The interface between the two is a novel operational semantics for causal consistency. We have verified the causal consistency of two key-value store implementations from the literature using a novel proof technique. We have also implemented a simple automatic model checker for the correctness of client programs. The two independently verified results for the implementations and clients can be composed to conclude the correctness of any of the programs when executed with any of the implementations. We have developed and checked our framework in Coq, extracted it to OCaml, and built executable stores.