Local Computation Algorithms Research Articles

A radiometric and rotational invariant feature descriptor for multimodal remote sensing image matching using the monogenic signal

ABSTRACT Multimodal remote sensing image matching is still a challenging task, and its matching performance will highly influence the subsequent applications, such as image fusion, image mosaic and change detection. To tackle this problem, we propose a radiometric and rotational invariant descriptor (RRID) using the monogenic signal for multimodal image matching. First of all, a multiscale feature asymmetry measurement is proposed to obtain more reliable detected points, in which the multiscale feature asymmetry can be computed from the intermediate results from the monogenic signal; then a multiscale local phase orientation computation algorithm is designed for the main orientation assignment of each keypoint, in which the local phase orientation can also be provided by the monogenic signal construction; finally, a circular local window around each keypoint is extracted, a histogram of local phase orientations weighted by phase congruency is calculated for the log-polar feature description. RRID is compared with other state-of-the-art multimodal image matching methods on three publicly available datasets. Experimental results have demonstrated that our proposed method outperforms the compared methods in terms of precision, recall, and F1-measure criteria and also has achieved the lowest RMSEs.

A blockchain-empowered framework for decentralized trust management in Internet of Battlefield Things

The security of the Internet of Battlefield Things (IoBT) is greatly challenged by malicious intrusions from external environments. To protect IoBT from such intrusions, it is crucial to implement trust management (TM) at the node level. However, the decentralized and dynamic nature of IoBT means that participating nodes have no predetermined trust relationships. To address this issue, we propose a blockchain-empowered framework to achieve decentralized TM in IoBT. We begin by introducing a network model that integrates the space and ground segments with portable ping-pong stations. In the absence of fixed infrastructure, these stations enable rapid networking among combat units in IoBT. We also leverage these stations to form a blockchain network that manages decentralized trusts among IoBT nodes. Our blockchain-empowered TM framework consists of three algorithmic components: (i) Local Trust Computation: each IoBT node uses a local trust computation algorithm to compute the local trusts of its neighboring nodes; (ii) Global Trust Aggregation: portable ping-pong stations use a global trust aggregation algorithm to aggregate the global trusts of IoBT nodes; (iii) Blockchain Consensus Process: the global trusts of IoBT nodes are updated to the blockchain. We have also developed a new consensus algorithm that incentivizes blockchain nodes to proactively maintain the real trusts of IoBT nodes. We conducted several simulations incorporating different attack models of malicious nodes and system setups to comprehensively evaluate the performance of our TM framework. The simulation results demonstrate that our blockchain-empowered decentralized TM effectively suppresses the probability of successful attacks and thus improves the security of IoBT. In summary, our proposed framework offers a promising solution for achieving decentralized TM in IoBT, and we believe that it has the potential to significantly enhance the security of this rapidly developing field.

Making inferences in incomplete Bayesian networks: A Dempster-Shafer belief function approach

How do you make inferences from a Bayesian network (BN) model with missing information? For example, we may not have priors for some variables or may not have conditionals for some states of the parent variables. It is well-known that the Dempster-Shafer (D-S) belief function theory is a generalization of probability theory. So, a solution is to embed an incomplete BN model in a D-S belief function model, omit the missing data, and then make inferences from the belief function model. We will demonstrate this using an implementation of a local computation algorithm for D-S belief function models called the “Belief function machine.” One advantage of this approach is that we get interval estimates of the probabilities of interest. Using Laplacian (equally likely) or maximum entropy priors or conditionals for missing data in a BN may lead to point estimates for the probabilities of interest, masking the uncertainty in these estimates. Bayesian reasoning cannot reason from an incomplete model. A Bayesian sensitivity analysis of the missing parameters is not a substitute for a belief-function analysis.

MEC Computation Offloading-Based Learning Strategy in Ultra-Dense Networks

Mobile edge computing (MEC) has the potential to realize intensive applications in 5G networks. Through migrating intensive tasks to edge servers, MEC can expand the computing power of wireless networks. Fifth generation networks need to meet service requirements, such as wide coverage, high capacity, low latency and low power consumption. Therefore, the network architecture of MEC combined with ultra-dense networks (UDNs) will become a typical model in the future. This paper designs a MEC architecture in a UDN, which is our research background. First, the system model is established in the UDN, and the optimization problems is proposed. Second, the action classification (AC) algorithm is utilized to filter the effective action in Q-learning. Then, the optimal computation offloading strategy and resource allocation scheme are obtained using a deep reinforcement learning-based AC algorithm, which is known as the DQN-AC algorithm. Finally, the simulation experiments show that the proposed DQN-AC algorithm can effectively reduce the system weighted cost compared with the full local computation algorithm, full offloading computation algorithm and Q-learning algorithm.

Logarithmic Communication for Distributed Optimization in Multi-Agent Systems

Classically, the design of multi-agent systems is approached using techniques from distributed optimization such as dual descent and consensus algorithms. Such algorithms depend on convergence to global consensus before any individual agent can determine its local action. This leads to challenges with respect to communication overhead and robustness, and improving algorithms with respect to these measures has been a focus of the community for decades. This paper presents a new approach for multi-agent system design based on ideas from the emerging field of local computation algorithms. The frameworkwe develop, LOcal Convex Optimization (LOCO), is the first local computation algorithm for convex optimization problems and can be applied in a wide-variety of settings. We demonstrate the generality of the framework via applications to Network Utility Maximization (NUM) and the distributed training of Support Vector Machines (SVMs), providing numerical results illustrating the improvement compared to classical distributed optimization approaches in each case.

Logarithmic Communication for Distributed Optimization in Multi-Agent Systems

Classically, the design of multi-agent systems is approached using techniques from distributed optimization such as dual descent and consensus algorithms. Such algorithms depend on convergence to global consensus before any individual agent can determine its local action. This leads to challenges with respect to communication overhead and robustness, and improving algorithms with respect to these measures has been a focus of the community for decades. This paper presents a new approach for multi-agent system design based on ideas from the emerging field of local computation algorithms. The framework we develop, LOcal Convex Optimization (LOCO), is the first local computation algorithm for convex optimization problems and can be applied in a wide-variety of settings. We demonstrate the generality of the framework via applications to Network Utility Maximization (NUM) and the distributed training of Support Vector Machines (SVMs), providing numerical results illustrating the improvement compared to classical distributed optimization approaches in each case.

Distributed Optimization via Local Computation Algorithms

We propose a new approach for distributed optimization based on an emerging area of theoretical computer science -- local computation algorithms. The approach is fundamentally different from existing methodologies and provides a number of benefits, such as robustness to link failure and adaptivity in dynamic settings. Specifically, we develop an algorithm, LOCO, that given a convex optimization problem P with n variables and a "sparse" linear constraint matrix with m constraints, provably finds a solution as good as that of the best online algorithm for P using only O(log(n+m)) messages with high probability. The approach is not iterative and communication is restricted to a localized neighborhood. In addition to analytic results, we show numerically that the performance improvements over classical approaches for distributed optimization are significant, e.g., it uses orders of magnitude less communication than ADMM.

Constant-Time Local Computation Algorithms

Local computation algorithms (LCAs) produce small parts of a single (possibly approximate) solution to a given search problem using time and space sublinear in the size of the input. In this work we present LCAs whose time complexity (and usually also space complexity) is independent of the input size. Specifically, we give (1) a (1 − 𝜖)-approximation LCA to the maximum weight acyclic edge set, (2) LCAs for approximating multicut and integer multicommodity flow on trees, and (3) a local reduction of weighted matching to any unweighted matching LCA, such that the running time of the weighted matching LCA is d times (where d is the maximal degree) the running time of the unweighted matching LCA, (and therefore independent of the edge weight function).

Local Computation Mechanism Design

We introduce the notion of local computation mechanism design —designing game-theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments. We present local computation mechanisms for two classical game-theoretical problems: stable matching and job scheduling. For stable matching, some of our techniques may have implications to the global (non-LCA (Local Computation Algorithm)) setting. Specifically, we show that when the men’s preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

New techniques and tighter bounds for local computation algorithms

Given an input x and a search problem F, local computation algorithms (LCAs) implement access to specified locations of y in a legal output y∈F(x), using polylogarithmic time and space. Parnas and Ron [27] and Mansour et al. [19] showed how to convert certain distributed and online algorithms to LCAs, respectively. In this work, we expand on those lines of work and develop new techniques for designing LCAs and bounding their space and time complexity.

Local Computation Algorithms for Graphs of Non-constant Degrees

In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with subexponential dependence on d, while maintaining polylogarithmic dependence on n. We present:a randomized LCA for computing maximal independent sets whose time and space complexities are quasi-polynomial in d and polylogarithmic in n;for constant $$\varepsilon > 0$$?>0, a randomized LCA that provides a $$(1-\varepsilon )$$(1-?)-approximation to maximum matching with high probability, whose time and space complexities are polynomial in d and polylogarithmic in n.

Falcon

Graph algorithms have been shown to possess enough parallelism to keep several computing resources busy—even hundreds of cores on a GPU. Unfortunately, tuning their implementation for efficient execution on a particular hardware configuration of heterogeneous systems consisting of multicore CPUs and GPUs is challenging, time consuming, and error prone. To address these issues, we propose a domain-specific language (DSL), Falcon, for implementing graph algorithms that (i) abstracts the hardware, (ii) provides constructs to write explicitly parallel programs at a higher level, and (iii) can work with general algorithms that may change the graph structure (morph algorithms). We illustrate the usage of our DSL to implement local computation algorithms (that do not change the graph structure) and morph algorithms such as Delaunay mesh refinement, survey propagation, and dynamic SSSP on GPU and multicore CPUs. Using a set of benchmark graphs, we illustrate that the generated code performs close to the state-of-the-art hand-tuned implementations.

Enabling local computation for partially ordered preferences

Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the Shafer---Shenoy framework and thus benefit from local computation algorithms. It also provides several examples of such scales, thus showing that each of the algebraic structures explored here is of interest.

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Graphical Models for Genetic Analyses

This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships between various local computation algorithms which have been developed within the hitherto mostly separate areas of graphical models and genetics. The potential of graphical models is explored and illustrated through a number of example applications where the genetic element is substantial or dominating.