OpenRaiser/Intern-Atlas huggingface dataset:
Fast clique minor generation in Chimera qubit connectivity graphs
Venue: arXiv cs.DM 2020
Year: 2020

The current generation of D-Wave quantum annealing processor is designed to minimize the energy of an Ising spin configuration whose pairwise interactions lie on the edges of a {\em Chimera} graph $\mathcal C_{M,N,L}$. In order to solve an Ising spin problem with arbitrary pairwise interaction structure, the corresponding graph must be minor-embedded into a Chimera graph. We define a combinatorial class of {\em native clique minors} in Chimera graphs with vertex images of uniform, near minimal size, and provide a polynomial-time algorithm that finds a maximum native clique minor in a given induced subgraph of a Chimera graph. These minors allow improvement over recent work and have immediate practical applications in the field of quantum annealing.
Applied Choreographies
Venue: arXiv cs.PL 2020
Year: 2020

Choreographic Programming is a correct-by-construction paradigm where a compilation procedure synthesises deadlock-free, concurrent, and distributed communicating processes from global, declarative descriptions of communications, called choreographies. Previous work used choreographies for the synthesis of programs. Alas, there is no formalisation that provides a chain of correctness from choreographies to their implementations. This problem originates from the gap between existing theoretical models, which abstract communications using channel names (à la CCS/π-calculus), and their implementations, which use low-level mechanisms for message routing. As a solution, we propose the theoretical framework of Applied Choreographies. In the framework, developers write choreographies in a language that follows the standard syntax and name-based communication semantics of previous works. Then, they use a compilation procedure to transform a choreography into a low-level, implementation-adherent calculus of Service-Oriented Computing (SOC). To manage the complexity of the compilation, we divide its formalisation and proof in three stages, respectively dealing with: a) the translation of name-based communications into their SOC equivalents (namely, using correlation mechanisms based on message data); b) the projection of a choreography into a composition of partial, single-participant choreographies (towards their translation into SOC processes); c) the translation of partial choreographies and the distribution of choreography-level state into SOC processes. We provide results of behavioural correspondence for each stage. Thus, given a choreography specification, we guarantee to synthesise its faithful and deadlock-free service-oriented implementation.
Building a Balanced k-d Tree with MapReduce
Venue: arXiv cs.DS 2020
Year: 2020

The original description of the k-d tree recognized that rebalancing techniques, such as are used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to obtain all of the data prior to building the tree then to build the tree via recursive subdivision of the data. One algorithm for building a balanced k-d tree finds the median of the data for each recursive subdivision of the data and builds the tree in O(n log n) time. A new algorithm builds a balanced k-d tree by presorting the data in each of k dimensions prior to building the tree, then preserves the order of the k presorts during recursive subdivision of the data and builds the tree in O(kn log n) time. This new algorithm is amenable to execution via MapReduce and permits building and searching a k-d tree that is represented as a distributed graph.
Strategic Decompositions of Normal Form Games: Zero-sum Games and Potential Games
Venue: arXiv cs.GT 2020
Year: 2020

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every player, the payoff differences between two strategies (holding other players' strategies fixed) are identical. A zero-sum equivalent game is a game that is strategically equivalent to a zero-sum game; a zero-sum equivalent potential game is a zero-sum equivalent game that is strategically equivalent to a common interest game. We also call a game "normalized" if the sum of one player's payoffs, given the other players' strategies, is always zero. We show that any normal form game can be uniquely decomposed into either (i) a zero-sum equivalent game and a normalized common interest game, or (ii) a zero-sum equivalent potential game, a normalized zero-sum game, and a normalized common interest game, each with distinctive equilibrium properties. For example, we show that two-player zero-sum equivalent games with finite strategy sets generically have a unique Nash equilibrium and that two-player zero-sum equivalent potential games with finite strategy sets generically have a strictly dominant Nash equilibrium.
Matching while Learning
Venue: arXiv cs.LG 2020
Year: 2020

We consider the problem faced by a service platform that needs to match limited supply with demand but also to learn the attributes of new users in order to match them better in the future. We introduce a benchmark model with heterogeneous "workers" (demand) and a limited supply of "jobs" that arrive over time. Job types are known to the platform, but worker types are unknown and must be learned by observing match outcomes. Workers depart after performing a certain number of jobs. The expected payoff from a match depends on the pair of types and the goal is to maximize the steady-state rate of accumulation of payoff. Though we use terminology inspired by labor markets, our framework applies more broadly to platforms where a limited supply of heterogeneous products is matched to users over time. Our main contribution is a complete characterization of the structure of the optimal policy in the limit that each worker performs many jobs. The platform faces a trade-off for each worker between myopically maximizing payoffs (exploitation) and learning the type of the worker (exploration). This creates a multitude of multi-armed bandit problems, one for each worker, coupled together by the constraint on availability of jobs of different types (capacity constraints). We find that the platform should estimate a shadow price for each job type, and use the payoffs adjusted by these prices, first, to determine its learning goals and then, for each worker, (i) to balance learning with payoffs during the "exploration phase," and (ii) to myopically match after it has achieved its learning goals during the "exploitation phase."
An Approximate Dynamic Programming Approach to Adversarial Online Learning
Venue: arXiv cs.GT 2020
Year: 2020

We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games prominently arise in the analysis of regret in repeated decision-making in adversarial environments, also known as adversarial online learning. At the core of our approach is a characterization of the lower Pareto frontier of the set of expected losses that a player can guarantee in these games as the unique fixed point of a set-valued dynamic programming operator. When applied to the problem of regret minimization with discounted losses, our approach yields algorithms that achieve markedly improved performance bounds compared to off-the-shelf online learning algorithms like Hedge. These results thus suggest the significant potential of ADP-based approaches in adversarial online learning.
Algorithms and Identities for B$\acute{e}$zier curves via Post Quantum Blossom
Venue: arXiv cs.GR 2020
Year: 2020

In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post quantum blossom, various new identities and formulae expressing the monomials in terms of the post quantun Bernstein basis functions and a post quantun variant of Marsden's identity are investigated. For each post quantum B$\acute{e}$zier curves of degree $m,$ a collection of $m!$ new, affine invariant, recursive evaluation algorithms are derived.
Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications
Venue: arXiv cs.CG 2020
Year: 2020

We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include $L_p$-norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses $O(n \log^3 n)$ storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat and Sharir that required $O(n^\varepsilon)$ time for an update and $O(\log n)$ time for a query [SICOMP, 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an $O(n^\varepsilon)$ factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph.
Adding Context to Concept Trees
Venue: arXiv cs.AI 2020
Year: 2020

A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of bringing brain-like and computer systems closer together. Concept Trees can grow from the semi-structured sources when consistent sequences of concepts are presented. Each tree ideally represents a single cohesive concept and the trees can link with each other for navigation and semantic purposes. The trees are therefore also a type of semantic network and would benefit from having a consistent level of context for each node. A consistent build process is managed through a 'counting rule' and some other rules that can normalise the database structure. This restricted structure can then be complimented and enriched by the more dynamic context. It is also suggested to use the linking structure of the licas system [15] as a basis for the context links, where the mathematical model is extended further to define this. A number of tests have demonstrated the soundness of the architecture. Building the trees from text documents shows that the tree structure could be inherent in natural language. Then, two types of query language are described. Both of these can perform consistent query processes to return knowledge to the user and even enhance the query with new knowledge. This is supported even further with direct comparisons to a cognitive model, also being developed by the author.
Hierarchical Data Generator based on Tree-Structured Stick Breaking Process for Benchmarking Clustering Methods
Venue: arXiv cs.CV 2020
Year: 2020

Object Cluster Hierarchies is a new variant of Hierarchical Cluster Analysis that gains interest in the field of Machine Learning. Being still at an early stage of development, the lack of tools for systematic analysis of Object Cluster Hierarchies inhibits its further improvement. In this paper we address this issue by proposing a generator of synthetic hierarchical data that can be used for benchmarking Object Cluster Hierarchy methods. The article presents a thorough empirical and theoretical analysis of the generator and provides guidance on how to control its parameters. Conducted experiments show the usefulness of the data generator that is capable of producing a wide range of differently structured data. Further, benchmarking datasets that mirror the most common types of hierarchies are generated and made available to the public, together with the developed generator (http://kio.pwr.edu.pl/?page\_id=396).
Precise neural network computation with imprecise analog devices
Venue: arXiv cs.NE 2020
Year: 2020

The operations used for neural network computation map favorably onto simple analog circuits, which outshine their digital counterparts in terms of compactness and efficiency. Nevertheless, such implementations have been largely supplanted by digital designs, partly because of device mismatch effects due to material and fabrication imperfections. We propose a framework that exploits the power of deep learning to compensate for this mismatch by incorporating the measured device variations as constraints in the neural network training process. This eliminates the need for mismatch minimization strategies and allows circuit complexity and power-consumption to be reduced to a minimum. Our results, based on large-scale simulations as well as a prototype VLSI chip implementation indicate a processing efficiency comparable to current state-of-art digital implementations. This method is suitable for future technology based on nanodevices with large variability, such as memristive arrays.
Modelling resource contention in multi-robot task allocation problems with uncertain timing
Venue: arXiv cs.MA 2020
Year: 2020

This paper proposes an analytical framework for modelling resource contention in multi-robot systems, where the travel times and task durations are uncertain. It uses several approximation methods to quickly and accurately calculate the probability distributions describing the times at which the tasks start and finish. Specific contributions include exact and fast approximation methods for calculating the probability of a set of independent normally distributed random events occurring in a given order, a method for calculating the most likely and n-th most likely orders of occurrence for a set of independent normally distributed random events that have equal standard deviations, and a method for approximating the conditional probability distributions of the events given a specific order of the events. The complete framework is shown to be faster than a Monte Carlo approach for the same accuracy in two multi-robot task allocation problems. In addition, the importance of incorporating uncertainty is demonstrated through a comparison with a deterministic method. This is a general framework that is agnostic to the optimisation method and objective function used, and is applicable to a wide range of problems.
KSR: A Semantic Representation of Knowledge Graph within a Novel Unsupervised Paradigm
Venue: arXiv cs.LG 2020
Year: 2020

Knowledge representation is a long-history topic in AI, which is very important. A variety of models have been proposed for knowledge graph embedding, which projects symbolic entities and relations into continuous vector space. However, most related methods merely focus on the data-fitting of knowledge graph, and ignore the interpretable semantic expression. Thus, traditional embedding methods are not friendly for applications that require semantic analysis, such as question answering and entity retrieval. To this end, this paper proposes a semantic representation method for knowledge graph \textbf{(KSR)}, which imposes a two-level hierarchical generative process that globally extracts many aspects and then locally assigns a specific category in each aspect for every triple. Since both aspects and categories are semantics-relevant, the collection of categories in each aspect is treated as the semantic representation of this triple. Extensive experiments show that our model outperforms other state-of-the-art baselines substantially.
Duplication of Windows Services
Venue: arXiv cs.OS 2020
Year: 2020

OS-level virtualization techniques virtualize system resources at the system call interface, has the distinct advantage of smaller run-time resource requirements as compared to HAL-level virtualization techniques, and thus forms an important building block for virtualizing parallel and distributed applications such as a HPC clusters. Because the Windows operating system puts certain critical functionalities in privileged user-level system service processes, a complete OS-level virtualization solution for the Windows platform requires duplication of such Windows service as Remote Procedure Call Server Service (RPCSS). As many implementation details of the Windows system services are proprietary, duplicating Windows system services becomes the key technical challenge for virtualizing the Windows platform at the OS level. Moreover, as a core component of cloud computing, IIS web server-related services need to be duplicated in containers (i.e., OS-level virtual machines), but so far there is no such scheme. In this paper, we thoroughly identify all issues that affect service duplication, and then propose the first known methodology to systematically duplicate both system and ordinary Windows services. Our experiments show that the methodology can duplicate a set of system and ordinary services on different versions of Windows OS.
Analysis of the Self Projected Matching Pursuit Algorithm
Venue: arXiv cs.CV 2020
Year: 2020

The convergence and numerical analysis of a low memory implementation of the Orthogonal Matching Pursuit greedy strategy, which is termed Self Projected Matching Pursuit, is presented. This approach renders an iterative way of solving the least squares problem with much less storage requirement than direct linear algebra techniques. Hence, it appropriate for solving large linear systems. The analysis highlights its suitability within the class of well posed problems.
Universal Hinge Patterns for Folding Strips Efficiently into Any Grid Polyhedron
Venue: arXiv cs.CG 2020
Year: 2020

We present two universal hinge patterns that enable a strip of material to fold into any connected surface made up of unit squares on the 3D cube grid--for example, the surface of any polycube. The folding is efficient: for target surfaces topologically equivalent to a sphere, the strip needs to have only twice the target surface area, and the folding stacks at most two layers of material anywhere. These geometric results offer a new way to build programmable matter that is substantially more efficient than what is possible with a square $N \times N$ sheet of material, which can fold into all polycubes only of surface area $O(N)$ and may stack $Θ(N^2)$ layers at one point. We also show how our strip foldings can be executed by a rigid motion without collisions (albeit assuming zero thickness), which is not possible in general with 2D sheet folding. To achieve these results, we develop new approximation algorithms for milling the surface of a grid polyhedron, which simultaneously give a 2-approximation in tour length and an 8/3-approximation in the number of turns. Both length and turns consume area when folding a strip, so we build on past approximation algorithms for these two objectives from 2D milling.
Sequential Solutions in Machine Scheduling Games
Venue: arXiv cs.GT 2020
Year: 2020

We consider the classical machine scheduling, where $n$ jobs need to be scheduled on $m$ machines, and where job $j$ scheduled on machine $i$ contributes $p_{i,j}\in \mathbb{R}$ to the load of machine $i$, with the goal of minimizing the makespan, i.e., the maximum load of any machine in the schedule. We study inefficiency of schedules that are obtained when jobs arrive sequentially one by one, and the jobs choose themselves the machine on which they will be scheduled, aiming at being scheduled on a machine with small load. We measure the inefficiency of a schedule as the ratio of the makespan obtained in the worst-case equilibrium schedule, and of the optimum makespan. This ratio is known as the \emph{sequential price of anarchy}. We also introduce two alternative inefficiency measures, which allow for a favorable choice of the order in which the jobs make their decisions. As our first result, we disprove the conjecture of Hassin and Yovel claiming that the sequential price of anarchy for $m=2$ machines is at most 3. We show that the sequential price of anarchy grows at least linearly with the number $n$ of players, i.e., we show that $SPoA = Ω(n)$. Furthermore, we show that there exists an order of the jobs, resulting in makespan that is at most linearly larger than the optimum makespan. To the end, we show that if an authority can change the order of the jobs adaptively to the decisions made by the jobs so far (but cannot influence the decisions of the jobs), then there exists an adaptive ordering in which the jobs end up in an optimum schedule.
Dynamic Network Reconstruction from Heterogeneous Datasets
Venue: arXiv cs.SY 2020
Year: 2020

Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all collected data simultaneously to infer the underlying dynamic network. This paper addresses the reconstruction of dynamic networks from heterogeneous datasets under the assumption that underlying networks share the same Boolean structure across all experiments. Parametric models for dynamical structure functions are derived to describe causal interactions between measured variables. Multiple datasets are integrated into one regression problem with additional demands of group sparsity to assure network sparsity and structure consistency. To acquire structured group sparsity, we propose a sampling-based method, together with extended versions of l1 methods and sparse Bayesian learning. The performance of the proposed methods is benchmarked in numerical simulation. In summary, this paper presents efficient methods on network reconstruction from multiple experiments, and reveals practical experience that could guide applications.
LogLog-Beta and More: A New Algorithm for Cardinality Estimation Based on LogLog Counting
Venue: arXiv cs.DS 2020
Year: 2020

The information presented in this paper defines LogLog-Beta. LogLog-Beta is a new algorithm for estimating cardinalities based on LogLog counting. The new algorithm uses only one formula and needs no additional bias corrections for the entire range of cardinalities, therefore, it is more efficient and simpler to implement. Our simulations show that the accuracy provided by the new algorithm is as good as or better than the accuracy provided by either of HyperLogLog or HyperLogLog++. In addition to LogLog-Beta we also provide another one-formula estimator for cardinalities based on order statistics, a modification of an algorithm developed by Lumbroso.