We consider large-scale Markov decision processes (MDPs) with a time-consistent risk measure of variability in cost under the risk-aware MDP paradigm. Previous studies showed that risk-aware MDPs, based on a minimax a...
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We consider large-scale Markov decision processes (MDPs) with a time-consistent risk measure of variability in cost under the risk-aware MDP paradigm. Previous studies showed that risk-aware MDPs, based on a minimax approach to handling risk, can be solved using dynamic programming for small-to medium-sized problems. However, due to the "curse of dimensionality," MDPs that model real-life problems are typically prohibitively large for such approaches. In this technical note, we employ an approximate dynamic programming approach and develop a family of simulation-based algorithms to approximately solve large-scale risk-aware MDPs with time-consistent risk measures. In parallel, we develop a unified convergence analysis technique to derive sample complexity bounds for this new family of algorithms.
Discovering frequent patterns over event sequences is an important data mining problem. Existing methods typically require multiple passes over the data, rendering them unsuitable for streaming contexts. We present th...
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Discovering frequent patterns over event sequences is an important data mining problem. Existing methods typically require multiple passes over the data, rendering them unsuitable for streaming contexts. We present the first streaming algorithm for mining frequent patterns over a window of recent events in the stream. We derive approximation guarantees for our algorithm in terms of: (i) the separation of frequent patterns from the infrequent ones, and (ii) the rate of change of stream characteristics. Our parameterization of the problem provides a new sweet spot in the tradeoff between making distributional assumptions over the stream and algorithmic efficiencies of mining. We illustrate how this yields significant benefits when mining practical streams from neuroscience and telecommunications logs.
Multiple sequence alignment is an important problem in computational molecular biology. Dynamic programming for optimal multiple alignment requires too much time to be practical. Although many algorithms for suboptima...
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Multiple sequence alignment is an important problem in computational molecular biology. Dynamic programming for optimal multiple alignment requires too much time to be practical. Although many algorithms for suboptimal alignment have been suggested, no "performance guarantees" algorithms have been known until recently. A computationally efficient approximation multiple alignment algorithm with guaranteed error bounds equal to the normalized communication cost of a corresponding graph is given in this paper. Recently, Altschul and Lipman [SIAM J. Appl. Math., 49 (1989), pp. 197-2091 used suboptimal alignments for reducing the computational complexity of the optimal alignment algorithm. This paper develops the Altschul-Lipman approach and demonstrates that bounds for optimal multiple alignment of k sequences can be derived from a solution of the maximum weighted matching problem in a k-vertex graph. Fast maximum matching algorithms allow efficient implementation of dynamic bounds for the multiple alignment problem.
This paper aims to study techniques for designing truthful mechanisms for a combinatorial optimization problem that might require composition algorithms. We show that the composition algorithm A o B is monotone if the...
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This paper aims to study techniques for designing truthful mechanisms for a combinatorial optimization problem that might require composition algorithms. We show that the composition algorithm A o B is monotone if the algorithm A and the algorithm B are both monotone. We apply this technique to the two-dimensional orthogonal knapsack problem with provable constant approximation bounds, improving the previous non constant results in [5]. Moreover, we show that the technique can also be applied to the heterogeneous multiple clusters scheduling problem, and, a truthful mechanism with provable approximation bounds was presented. (C) 2016 Elsevier B.V. All rights reserved.
We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we desig...
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We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a sublinear-time algorithm for approximating the number of triangles in a graph, where the algorithm is given query access to the graph. The allowed queries are degree queries, vertex -pair queries, and neighbor queries. We show that for any given approximation parameter 0 < epsilon < 1, the algorithm provides an estimate (t) over cap such that, with high constant probability, (1 - epsilon) . t < <(t)over cap> < (1 + epsilon) . t, where t is the number s12triangles in the graph G. The expected query complexity of the algorithm is ((n)(t1/3) + min{m, (m3/2)(t) }) . poly(log n, 1/epsilon), where n is the number of vertices in the graph and m is the number of edges. The expected running time of the algorithm is (n/(t)1/3 + m(3/2)/t) . poly(log n,1/epsilon) We also prove that Omega(n/(t)1/3 + min{m, m(3/2)/t}) queries are necessary, thus establishing that the query complexity of this algorithm is optimal up to the dependence on poly(log n, 1/epsilon).
In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferent...
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In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferentially with consideration of the reaction functions of all followers, while, at the lower level, each of the followers reacts optimally to the leader's strategy simultaneously by playing a Nash game. First, the optimal strategies for the leader and the followers are derived from down to the top, and these strategies are further shown to constitute the Stackelberg-Nash equilibrium points. Subsequently, to overcome the difficulty in calculating the equilibrium points analytically, we develop a novel two-level value iteration-based integral reinforcement learning (VI-IRL) algorithm that relies only upon partial information of system dynamics. We establish that the proposed method converges asymptotically to the equilibrium strategies under the weak coupling conditions. Moreover, we introduce effective termination criteria to guarantee the admissibility of the policy (strategy) profile obtained from a finite number of iterations of the proposed algorithm. In the implementation of our scheme, we employ neural networks (NNs) to approximate the value functions and invoke the least-squares methods to update the involved weights. Finally, the effectiveness of the developed algorithm is verified by two simulation examples.
In this paper, we consider the connected target coverage (CTC) problem with the objective of maximizing the network lifetime by scheduling sensors into multiple sets, each of which can maintain both target coverage an...
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In this paper, we consider the connected target coverage (CTC) problem with the objective of maximizing the network lifetime by scheduling sensors into multiple sets, each of which can maintain both target coverage and connectivity among all the active sensors and the sink. We model the CTC problem as a maximum cover tree (MCT) problem and prove that the MCT problem is NP-Complete. We determine an upper bound on the network lifetime for the MCT problem and then develop a (1 + w) H ((M) over cap) approximation algorithm to solve it, where w is an arbitrarily small number, H((M) over cap) = Sigma(1 <= i <=(M) over cap)(1/i) and (M) over cap is the maximum number of targets in the sensing area of any sensor. As the protocol cost of the approximation algorithm may be high in practice, we develop a faster heuristic algorithm based on the approximation algorithm called Communication Weighted Greedy Cover (CWGC) algorithm and present a distributed implementation of the heuristic algorithm. We study the performance of the approximation algorithm and CWGC algorithm by comparing them with the lifetime upper bound and other basic algorithms that consider the coverage and connectivity problems independently. Simulation results show that the approximation algorithm and CWGC algorithm perform much better than others in terms of the network lifetime and the performance improvement can be up to 45% than the best-known basic algorithm. The lifetime obtained by our algorithms is close to the upper bound. Compared with the approximation algorithm, the CWGC algorithm can achieve a similar performance in terms of the network lifetime with a lower protocol cost.
How can we effectively detect fake reviews or fraudulent links on a website? How can we spot communities that suddenly appear based on users' interactions? And how can we efficiently find the minimum cut in a larg...
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How can we effectively detect fake reviews or fraudulent links on a website? How can we spot communities that suddenly appear based on users' interactions? And how can we efficiently find the minimum cut in a large graph? All of these are related to the finding of dense subgraphs, a significant primitive problem in graph analysis with extensive applications across various domains. In this paper, we focus on formulating the problem of the densest subgraph detection and theoretically compare and contrast several correlated problems. Moreover, we propose a unified framework, GenDS , for the densest subgraph detection, provide some theoretical analysis based on the network flow and spectral graph theory, and devise simple and computationally efficient algorithms, SpecGDS and GepGDS , to solve it by leveraging the spectral properties and greedy search. We conduct thorough experiments on 40 real-world networks with up to 1.47 billion edges from various domains. We demonstrate that our SpecGDS yields up to 58.6 x speedup and achieves better or approximately equal-quality solutions for the densest subgraph detection compared to the baselines. GepGDS also reveals some properties of generalized eigenvalue problems for the GenDS . Also, our methods scale linearly with the graph size and are proven effective in applications such as finding collaborations that appear suddenly in an extensive, time-evolving co-authorship network.
We focus on throughput-maximizing, max-min fair, and proportionally fair scheduling problems for centralized cognitive radio networks. First, we propose a polynomial-time algorithm for the throughput-maximizing schedu...
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We focus on throughput-maximizing, max-min fair, and proportionally fair scheduling problems for centralized cognitive radio networks. First, we propose a polynomial-time algorithm for the throughput-maximizing scheduling problem. We then elaborate on certain special cases of this problem and explore their combinatorial properties. Second, we prove that the max-min fair scheduling problem is NP-Hard in the strong sense. We also prove that the problem cannot be approximated within any constant factor better than 2 unless P = NP. Additionally, we propose an approximation algorithm for the max-min fair scheduling problem with approximation ratio depending on the ratio of the maximum possible data rate to the minimum possible data rate of a secondary users. We then focus on the combinatorial properties of certain special cases and investigate their relation with various problems such as the multiple-knapsack, matching, terminal assignment, and Santa Claus problems. We then prove that the proportionally fair scheduling problem is NP-Hard in the strong sense and inapproximable within any additive constant less than log(4/3). Finally, we evaluate the performance of our approximation algorithm for the max-min fair scheduling problem via simulations. This approach sheds light on the complexity and combinatorial properties of these scheduling problems, which have high practical importance in centralized cognitive radio networks.
The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the...
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The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.
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