We explore a family of numerical methods, based on the Steffensen divided difference iterative algorithm, that do not evaluate the derivative of the objective functions. The family of methods achieves second-order con...
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We give the first local algorithm for computing multi-commodity flow and apply it to obtain a (1+∊)-approximate algorithm for computing a k-commodity flow on an expander with m edges in (m + ∊−3k3D)no(1) time, where D...
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We study a new model-free algorithm to compute Ε-optimal policies for average reward Markov decision processes, in the weakly communicating case. Given a generative model, our procedure combines a recursive sampling ...
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In the Correlation Clustering problem we are given n nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing ...
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In the Correlation Clustering problem we are given n nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing the minimum number of violated preferences. In certain cases, however, the preference between some pairs may be too important to be violated. The constrained version of this problem specifies pairs of nodes that must be in the same cluster as well as pairs that must not be in the same cluster (hard constraints). The output clustering has to satisfy all hard constraints while minimizing the number of violated preferences. Constrained Correlation Clustering is APX-Hard and has been approximated within a factor 3 by van Zuylen et al. [SODA’07]. Their algorithm is based on rounding an LP with Θ(n3) constraints, resulting in an Ω(n3ω) running time. In this work, using a more combinatorial approach, we show how to approximate this problem significantly faster at the cost of a slightly weaker approximation factor. In particular, our algorithm runs in Oe(n3) time (notice that the input size is Θ(n2)) and approximates Constrained Correlation Clustering within a factor 16. To achieve our result we need properties guaranteed by a particular influential algorithm for (unconstrained) Correlation Clustering, the CC-PIVOT algorithm. This algorithm chooses a pivot node u, creates a cluster containing u and all its preferred nodes, and recursively solves the rest of the problem. It is known that selecting pivots at random gives a 3-approximation. As a byproduct of our work, we provide a derandomization of the CC-PIVOT algorithm that still achieves the 3-approximation;furthermore, we show that there exist instances where no ordering of the pivots can give a (3 − Ε)-approximation, for any constant Ε. Finally, we introduce a node-weighted version of Correlation Clustering, which can be approximated within factor 3 using our insights on Constrained Correlation Clustering. A
This paper proposes an online scalar field estimation algorithm of unknown environments using a distributed Gaussian process framework in wireless sensor networks. While kernel-based Gaussian processes are commonly us...
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This paper proposes an online scalar field estimation algorithm of unknown environments using a distributed Gaussian process framework in wireless sensor networks. While kernel-based Gaussian processes are commonly used for scalar field estimation, their centralized nature makes it difficult to deal with a large number of measurements from sensor networks. To address this, recent advancements approximate kernel functions via E-dimensional nonlinear basis functions, improving scalability. However, this requires many basis functions for accurate approximation, increasing computational and communication complexities. We propose a Kalman filter-based distributed Gaussian process framework, which scales linearly with the number of basis functions and includes a new consensus protocol for efficient data transmission and rapid convergence. Simulation results demonstrate rapid consensus convergence and outstanding estimation accuracy achieved by the proposed algorithm. The scalability and efficiency of the proposed approach are further demonstrated by online dynamic environment estimation using sensor networks.
In this paper, we propose a novel parallel hierarchical Leiden-based algorithm for dynamic community detection. The algorithm, for a given batch update of edge insertions and deletions, partitions the network into com...
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With the increasing penetration of distributed energy resources, the traditional producer-centric electricity market is moving to a prosumer-centric market, where prosumers can trade with each other in an autonomous p...
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With the increasing penetration of distributed energy resources, the traditional producer-centric electricity market is moving to a prosumer-centric market, where prosumers can trade with each other in an autonomous pattern. However, there remain research gaps on the pricing and allocation of joint energy and reserves in an autonomous prosumer-centric market. This paper firstly designs a joint energy-reserve peer-to-peer (P2P) trading mechanism. The mechanism not only enables P2P energy trading but also quantifies the reserve cost and the value of flexibility. Then, a blockchain-based trading algorithm is proposed to implement a trustworthy prosumer-centric market. A pipelined delegated Byzantine fault tolerance (PDBFT) consensus algorithm is proposed to ensure robustness and improve the efficiency of the autonomous trading process. Numerical results show the effectiveness of the trading mechanism and the performance of the blockchain-based trading algorithm. Compared with only considering energy trading, the proposed mechanism reduces the total cost of the market by 16.03%. Compared with using the traditional practical Byzantine fault tolerance (PBFT) consensus algorithm, the computational time of market clearing on blockchain is decreased by 45.90%.
Average consensus has significant applications in dynamic load balancing and cooperative control of vehicle formations, where all the agents receive information from neighboring agents via communication network and up...
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Average consensus has significant applications in dynamic load balancing and cooperative control of vehicle formations, where all the agents receive information from neighboring agents via communication network and update their states to achieve an agreement. However, this approach would result in an undesirable disclosure on the initial states of agents to their neighbors. In this brief, we propose an accurate privacy preserving average consensus (APPAC) algorithm, where all the agents independently generate and transmit random numbers based on Paillier cryptosystem to conceal their initial states. Under the proposed APPAC algorithm, the accurate average consensus is indeed achieved. Besides, the necessary and sufficient conditions that initial states can be inferred are also discussed. Extensive simulations are conducted to demonstrate the effectiveness of the proposed algorithm.
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, w...
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We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natu...
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