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We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a…

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

Record linkage is aimed at the accurate and efficient identification of records that represent the same entity within or across disparate databases. It is a fundamental task in data integration and increasingly required for accurate…

Link and sign prediction in complex networks bring great help to decision-making and recommender systems, such as in predicting potential relationships or relative status levels. Many previous studies focused on designing the special…

We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…

While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…

Regularities in strings are often related to periods and covers, which have extensively been studied, and algorithms for their efficient computation have broad application. In this paper we concentrate on computing cyclic regularities of…

Accurate and efficient record linkage is an open challenge of particular relevance to Australian Government Agencies, who recognise that so-called wicked social problems are best tackled by forming partnerships founded on large-scale data…

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…

Lack of numerical precision in control software -- in particular, related to trajectory computation -- can lead to incorrect results with costly or even catastrophic consequences. Various tools have been proposed to analyze the precision of…

Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not…

We give an algorithm for finding network encoding and decoding equations for error-free multicasting networks with multiple sources and sinks. The algorithm given is efficient (polynomial complexity) and works on any kind of network…

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…

Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…