We show that the 2-Opt and 3-Opt heuristics for the traveling salesman problem (TSP) on the complete graph K. produce a solution no worse than the average cost of a tour in K. in a polynomial number of iterations. As ...
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We show that the 2-Opt and 3-Opt heuristics for the traveling salesman problem (TSP) on the complete graph K. produce a solution no worse than the average cost of a tour in K. in a polynomial number of iterations. As a consequence, we get that the domination numbers of the 2-Opt, 3-Opt, Carlier-Villon, Shortest Path Ejection Chain, and Lin-Kernighan heuristics are all at least (n - 2)!/2. The domination number of the Christofides heuristic is shown to be no more than [n/2]!, and for the Double Tree heuristic and a variation of the Christofides heuristic the domination numbers are shown to be one (even if the edge costs satisfy the triangle inequality). Further, unless P = NP no polynomial time approximation algorithm exists for the TSP on the complete digraph (K) over right arrow (n) with domination number at least (n - 1)! - k for any constant k or with domination number at least (n - 1)! - ((k/(k + 1))(n + r))! - 1 for any non-negative constants r and k such that (n + r) equivalent to 0 mod (k + 1). The complexities of finding the median value of costs of all the tours in (K) over right arrow (n) and of similar problems are also studied.
This paper examines two scheduling problems with job delivery coordination, in which each job demands different amount of storage space during transportation. For the first problem, in which jobs are processed on a si...
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This paper examines two scheduling problems with job delivery coordination, in which each job demands different amount of storage space during transportation. For the first problem, in which jobs are processed on a single machine and delivered by one vehicle to a customer, we present a best possible approximation algorithm with a worst-case ratio arbitrarily close to 3/2. For the second problem, which differs from the first problem in that jobs are processed by two parallel machines, we give an improved algorithm with a worst-case ratio 5/3. (c) 2006 Elsevier B.V. All rights reserved.
In order to extract useful information from data streams, incremental learning has been introduced in more and more data mining algorithms. For instance, a self-organizing incremental neural network (SOINN) has been p...
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In order to extract useful information from data streams, incremental learning has been introduced in more and more data mining algorithms. For instance, a self-organizing incremental neural network (SOINN) has been proposed to extract a topological structure that consists of one or more neural networks to closely reflect the data distribution of data streams. However, SOINN has the tradeoff between deleting previously learned nodes and inserting new nodes, i.e., the stability-plasticity dilemma. Therefore, it is not guaranteed that the topological structure obtained by the SOINN will closely represent data distribution. For solving the stability-plasticity dilemma, we propose a Gaussian membership-based SOINN (Gm-SOINN). Unlike other SOINN-based methods that allow only one node to be identified as a "winner" (the nearest node), the Gm-SOINN uses a Gaussian membership to indicate to which degree the node is a winner. Hence, the Gm-SOINN avoids the topological structure that cannot represent the data distribution because previously learned nodes overly deleted or noisy nodes inserted. In addition, an evolving Gaussian mixture model is integrated into the Gm-SOINN to estimate the density distribution of nodes, thereby avoiding the wrong connection between two nodes. Experiments involving both artificial and real-world data sets indicate that our proposed Gm-SOINN achieves better performance than other topology learning methods.
A simple rational interpolation method is given for estimating a frequency response matrix. The method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the su...
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A simple rational interpolation method is given for estimating a frequency response matrix. The method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms. When coupled with a pole cancellation method, the resulting interpolation algorithm is accurate and efficient. Somewhat surprisingly, the error in this procedure has the form of a modified response matrix, which means that the interpolation algorithm can be used to approximate both the response matrix and the error.
We propose a game-theory-based deep-learning tracking control scheme to enable a holonomic flying system to perform an autonomous trajectory tracking task, when considering saturating actuators, adversarial inputs, an...
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We propose a game-theory-based deep-learning tracking control scheme to enable a holonomic flying system to perform an autonomous trajectory tracking task, when considering saturating actuators, adversarial inputs, and nonquadratic cost functionals. The problem is formulated as a two-player zero-sum game, whose online solution is computed by learning the saddle point strategies in real time. Three approximators, namely a critic and two actors, are tuned online using data generated in real time along the system trajectories. The adaptive control character of the algorithm requires a persistence of excitation condition to be a priori validated, which is relaxed by using. a deep-learning approach, based on experience replay with multiple layers. A robustifying control term is added to eliminate the effect of residual errors, leading to asymptotic stability of the equilibrium point of the closed-loop system. A simulation of a target tracking application, where the measurements available to the aerial system are perturbed by persistent adversaries, is performed to validate the effectiveness of the proposed approach.
We study bottleneck labeled optimization problems arising in the context of graph theory. This long-established model partitions the set of edges into classes, each of which is identified by a unique color. The generi...
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We study bottleneck labeled optimization problems arising in the context of graph theory. This long-established model partitions the set of edges into classes, each of which is identified by a unique color. The generic objective is to construct a subgraph of prescribed structure (such as an s-t path, a spanning tree, or a perfect matching) while trying to minimize the maximum (or, alternatively, maximize the minimum) number of edges picked from any given color.
This article studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulator (LQR) problem. It is shown that Kleinman's policy iteration algorithm is small-...
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This article studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulator (LQR) problem. It is shown that Kleinman's policy iteration algorithm is small-disturbance input-to-state stable, a property that is stronger than Sontag's local input-to-state stability but weaker than global input-to-state stability. More precisely, whenever the error in each iteration is bounded and small, the solutions of the policy iteration algorithm are also bounded and enter a small neighborhood of the optimal solution of the LQR problem. Based on this result, an off-policy data-driven policy iteration algorithm for the LQR problem is shown to be robust when the system dynamics are subject to small additive unknown bounded disturbances. The theoretical results are validated by a numerical example.
Given a source node s and a target node t, the hitting probability tells us how likely an alpha-terminating random walk (which stops with probability $\alpha$alpha at each step) starting from s can hit t before it sto...
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Given a source node s and a target node t, the hitting probability tells us how likely an alpha-terminating random walk (which stops with probability $\alpha$alpha at each step) starting from s can hit t before it stops. This concept originates from the hitting time, a classic concept in random walks. In this paper, we focus on the group hitting probability (GHP) where the target is a set of nodes, measuring the node-to-group structural proximity. For this group version of the hitting probability, we present efficient algorithms for two types of GHP queries: the pairwise query which returns the GHP value of a target set T with respect to (w.r.t.) a source node s, and the top-k query which returns the top-k target sets with the largest GHP value w.r.t. a source node s. We first develop an efficient algorithm named SAMBA for the pairwise query, which is built on a group local push algorithm tailored for GHP, with rigorous analysis for correctness. Next, we show how to speed up SAMBA by combining the group local push algorithm with the Monte Carlo approach, where GHP brings new challenges as it might need to consider every hop of the random walk. We tackle this issue with a new formulation of the GHP and show how to provide approximation guarantees with a detailed theoretical analysis. With SAMBA as the backbone, we develop an iterative algorithm for top-k queries, which adaptively refines the bounds for the candidate target sets, and terminates as soon as it meets the stopping condition, thus saving unnecessary computational costs. We further present an optimization technique to accelerate the top-k query, improving its practical performance. Extensive experiments show that our solutions are orders of magnitude faster than their competitors.
This article is concerned with event-triggered consensus control for nonlinear multi-agent systems with unknown nonlinear functions, unmatched disturbances, and unmeasured state variables. A novel distributed control ...
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This article is concerned with event-triggered consensus control for nonlinear multi-agent systems with unknown nonlinear functions, unmatched disturbances, and unmeasured state variables. A novel distributed control algorithm is designed for high-order nonlinear multi-agent systems by using input-driven filters and defining dynamic feedback systems. In addition, the salient features of the proposed control algorithm are highlighted as follows: 1) our proposed control algorithm employs only local information from itself and its neighboring agents, 2) only a binary signal is transmitted to the actuator during the control process, and 3) the proposed control scheme avoids the use of approximate structures and lacks complex calculations. Finally, the simulation of the inverted pendulum verifies the validity of our theoretical findings.
In this paper we study the deployment of an Unmanned Aerial Vehicle (UAV) network that consists of multiple UAVs to provide emergent communication service for people who are trapped in a disaster area, where each UAV ...
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In this paper we study the deployment of an Unmanned Aerial Vehicle (UAV) network that consists of multiple UAVs to provide emergent communication service for people who are trapped in a disaster area, where each UAV is equipped with a base station that has limited computing capacity and power supply, and thus can only serve a limited number of people. Unlike most existing studies that focused on homogeneous UAVs, we consider the deployment of heterogeneous UAVs where different UAVs have different computing capacities. We study a problem of deploying K heterogeneous UAVs in the air to form a temporarily connected UAV network such that the network throughput - the number of users served by the UAVs, is maximized, subject to the constraint that the number of people served by each UAV is no greater than its service capacity. We then propose a novelO(root s/K) -approximation algorithm for the problem, where s is a given positive integer with 1 <= s <= K, e.g., s = 3. We also devise an improved heuristic, based on the approximation algorithm. We finally evaluate the performance of the proposed algorithms. Experimental results show that the numbers of users served by UAVs in the solutions delivered by the proposed algorithms are increased by 25% than state-of-the-arts.
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