A cross-technology benchmark for incremental graph queries

To cope with the increased complexity of systems, models are used to capture what is considered the essence of a system. Such models are typically represented as a graph, which is queried to gain insight into the modelled system. Often, the results of these queries need to be adjusted according to updated requirements and are therefore a subject of maintenance activities. It is thus necessary to support writing model queries with adequate languages. However, in order to stay meaningful, the analysis results need to be refreshed as soon as the underlying models change. Therefore, a good execution speed is mandatory in order to cope with frequent model changes. In this paper, we propose a benchmark to assess model query technologies in the presence of model change sequences in the domain of social media. We present solutions to this benchmark in a variety of 11 different tools and compare them with respect to explicitness of incrementalization, asymptotic complexity and performance.

A Public Key Cryptosystem Using Cyclotomic Matrices

Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this chapter, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the formulation of cyclotomic matrices correspond to a diophantine system. The strategy uses in cyclotomic matrices to design a one-way function. The result of a one-way function that is efficient to compute, however, is hard to process its inverse except if privileged information about the hidden entry is known. Also, we demonstrate that encryption and decryption can be efficiently performed with the asymptotic complexity of Oe2.373. Finally, we study the computational complexity of the cryptosystem.

Fast-forwarding quantum evolution

We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. In particular, we show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded in a model where quantum gates are exponentials of specific fermionic or bosonic operators, respectively. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, while not necessarily requiring methods that diagonalize the Hamiltonians efficiently. We further develop a connection between fast-forwarding and precise energy measurements that also accounts for polynomial improvements.

Dynaplex: analyzing program complexity using dynamically inferred recurrence relations

Being able to detect program runtime complexity is useful in many tasks (e.g., checking expected performance and identifying potential security vulnerabilities). In this work, we introduce a new dynamic approach for inferring the asymptotic complexity bounds of recursive programs. From program execution traces, we learn recurrence relations and solve them using pattern matching to obtain closed-form solutions representing the complexity bounds of the program. This approach allows us to efficiently infer simple recurrence relations that represent nontrivial, potentially nonlinear polynomial and non-polynomial, complexity bounds. We present Dynaplex, a tool that implements these ideas to automatically generate recurrence relations from execution traces. Our preliminary results on popular and challenging recursive programs show that Dynaplex can learn precise relations capturing worst-case complexity bounds (e.g., O ( n log n ) for mergesort, O (2 n ) for Tower of Hanoi and O ( n 1.58 ) for Karatsuba’s multiplication algorithm).

Stim: a fast stabilizer circuit simulator

This paper presents “Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the inverse of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.

The Hypervolume Indicator

The hypervolume indicator is one of the most used set-quality indicators for the assessment of stochastic multiobjective optimizers, as well as for selection in evolutionary multiobjective optimization algorithms. Its theoretical properties justify its wide acceptance, particularly the strict monotonicity with respect to set dominance, which is still unique of hypervolume-based indicators. This article discusses the computation of hypervolume-related problems, highlighting the relations between them, providing an overview of the paradigms and techniques used, a description of the main algorithms for each problem, and a rundown of the fastest algorithms regarding asymptotic complexity and runtime. By providing a complete overview of the computational problems associated to the hypervolume indicator, this article serves as the starting point for the development of new algorithms and supports users in the identification of the most appropriate implementations available for each problem.

Quantum Circuit Design of Toom 3-Way Multiplication

In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication. For the use in quantum computation, prior work considered the Toom-2.5 variant rather than the classically faster and more prominent Toom-3, primarily to avoid the nontrivial division operations inherent in the latter circuit. In this paper, we investigate the quantum circuit for Toom-3 multiplication, which is expected to give an asymptotically lower depth than the Toom-2.5 circuit. In particular, we designed the corresponding quantum circuit and adopted the sequence proposed by Bodrato to yield a lower number of operations, especially in terms of nontrivial division, which is reduced to only one exact division by 3 circuit per iteration. Moreover, to further minimize the cost of the remaining division, we utilize the unique property of the particular division circuit, replacing it with a constant multiplication by reciprocal circuit and the corresponding swap operations. Our numerical analysis shows that the resulting circuit indeed gives a lower asymptotic complexity in terms of Toffoli depth and qubit count compared to Toom-2.5 but with a large number of Toffoli gates that mainly come from realizing the division operation.

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methods to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell’s Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics (MHD) when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path. The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In the UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale. For plasma transport, the current scheme provides a smooth transition from particle-in-cell (PIC) method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

Efficient Rank-Based Diffusion Process with Assured Convergence

Visual features and representation learning strategies experienced huge advances in the previous decade, mainly supported by deep learning approaches. However, retrieval tasks are still performed mainly based on traditional pairwise dissimilarity measures, while the learned representations lie on high dimensional manifolds. With the aim of going beyond pairwise analysis, post-processing methods have been proposed to replace pairwise measures by globally defined measures, capable of analyzing collections in terms of the underlying data manifold. The most representative approaches are diffusion and ranked-based methods. While the diffusion approaches can be computationally expensive, the rank-based methods lack theoretical background. In this paper, we propose an efficient Rank-based Diffusion Process which combines both approaches and avoids the drawbacks of each one. The obtained method is capable of efficiently approximating a diffusion process by exploiting rank-based information, while assuring its convergence. The algorithm exhibits very low asymptotic complexity and can be computed regionally, being suitable to outside of dataset queries. An experimental evaluation conducted for image retrieval and person re-ID tasks on diverse datasets demonstrates the effectiveness of the proposed approach with results comparable to the state-of-the-art.

Statistically Efficient, Polynomial-Time Algorithms for Combinatorial Semi-Bandits

We consider combinatorial semi-bandits over a set of arms X \subset \0,1\ ^d where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound R(T) = O( d (łn m)^2 (łn T) / Δ_\min ) after T rounds, where m = \max_x \in X 1^\top x. However, ESCB it has computational complexity O(|X|), which is typically exponential in d, and cannot be used in large dimensions. We propose the first algorithm that is both computationally and statistically efficient for this problem with regret R(T) = O( d (łn m)^2 (łn T) / Δ_\min ) and computational asymptotic complexity O(δ_T^-1 poly(d)), where δ_T is a function which vanishes arbitrarily slowly. Our approach involves carefully designing AESCB, an approximate version of ESCB with the same regret guarantees. We show that, whenever budgeted linear maximization over X can be solved up to a given approximation ratio, AESCB is implementable in polynomial time O(δ_T^-1 poly(d)) by repeatedly maximizing a linear function over X subject to a linear budget constraint, and showing how to solve these maximization problems efficiently.