A multiplicative α-spanner H is a subgraph of G = (V,E) with the same vertices and fewer edges that preserves distances up to the factor α, i.e., dH(u, v) ≤ α dG(u, v) for all vertices u, v. While many algorithms ...
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In the article we describe a way of computation of mean time to failure of a system that consist of unrecoverable elements with constant failure rates (elements' modes of use and storage alternate in a cycle way)....
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We consider an energy harvesting sensor transmitting latency-sensitive data over a fading channel. We aim to find the optimal transmission scheduling policy that minimizes the packet queuing delay given the available ...
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We consider an energy harvesting sensor transmitting latency-sensitive data over a fading channel. We aim to find the optimal transmission scheduling policy that minimizes the packet queuing delay given the available harvested energy. We formulate the problem as a Markov decision process (MDP) over a state-space spanned by the transmitter's buffer, battery, and channel states, and analyze the structural properties of the resulting optimal value function, which quantifies the long-run performance of the optimal scheduling policy. We show that the optimal value function (i) is non-decreasing and has increasing differences in the queue backlog;(ii) is non-increasing and has increasing differences in the battery state;and (iii) is submodular in the buffer and battery states. Taking advantage of these structural properties, we derive an approximate value iteration algorithm that provides a controllable tradeoff between approximation accuracy, computational complexity, and memory, and we prove that it converges to a near-optimal value function and policy. Our numerical results confirm these properties and demonstrate that the resulting scheduling policies outperform a greedy policy in terms of queuing delay, buffer overflows, energy efficiency, and sensor outages.
Given a set D = {d1, ..., d(n)} of imprecise points modeled as disks, the minimum diameter problem is to locate a set P = {p(1), ..., p(n)} of fixed points, where p(i) is an element of d(i), such that the furthest dis...
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Given a set D = {d1, ..., d(n)} of imprecise points modeled as disks, the minimum diameter problem is to locate a set P = {p(1), ..., p(n)} of fixed points, where p(i) is an element of d(i), such that the furthest distance between any pair of points in P is as small as possible. This introduces a tight lower bound on the size of the diameter of any instance P. In this paper, we present a fully polynomial time approximation scheme (FPTAS) for computing the minimum diameter of a set of disjoint disks that runs in O(n(2)epsilon(-1)) time. Then we relax the disjointness assumption and we show that adjusting the presented FPTAS will cost O(n(2)epsilon(-1)) time. We also show that our results can be generalized in R-d when the dimension d is an arbitrary fixed constant. (C) 2020 Elsevier B.V. All rights reserved.
Software defined network (SDN) decouples control planes from data planes and integrates them into a logically centralized controller. With capture of the global view, the controller can dynamically and timely reply to...
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Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem in...
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The h-index is a metric used to measure the impact of a user in a publication setting, such as a member of a social network with many highly liked posts or a researcher in an academic domain with many highly cited pub...
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In this study, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. ...
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In this study, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product, and each customer either purchases a product or leaves the market after one transition. We study the assortment optimization problem under this model. Particularly, we show that it is NP-Hard even if the customer can transition from each product to at most two products. Despite the computational complexity, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is bounded. Our approximation algorithms are developed by invoking the submodularity arguments, or connecting the problem with maximum constraint satisfaction problem and applying randomized rounding techniques to its semidefinite programming relaxation. We also provide a tight worst-case performance bound for revenue-ordered assortments. In addition, we propose a compact mixed-integer program formulation, which is efficient for moderate size problems. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.
We study coverage problems in which, for a set of agents and a given threshold T, the goal is to select T subsets (of the agents) that, while satisfying combinatorial constraints, achieve fair and efficient coverage a...
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Let D be a set of straight-line segments in the plane, potentially crossing, and let c be a positive integer. We denote by P the union of the endpoints of the straight-line segments of D and of the intersection points...
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