First, a new concept, positive Hilbert spaces, is introduced and some fundamental inequalities which are applied to studying the properties of the resolvent operator associated for (gamma(G), lambda)-weak-GRD set-valu...
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First, a new concept, positive Hilbert spaces, is introduced and some fundamental inequalities which are applied to studying the properties of the resolvent operator associated for (gamma(G), lambda)-weak-GRD set-valued mappings are introduced and discussed in positive Hilbert spaces. Next, by using the resolvent operator and fixed point theory, an existence theorem and an approximation algorithm to solve a new class of general nonlinear ordered inclusions are established and suggested. In this field, the results obtained seem to be general in nature.
Over the past few decades, there has been a significant increase in the number of Earth observation satellites, and the area of ground targets requiring observation has also been expanding. To effectively utilize the ...
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Over the past few decades, there has been a significant increase in the number of Earth observation satellites, and the area of ground targets requiring observation has also been expanding. To effectively utilize the capabilities of these satellites and capture larger areas of ground targets, it has become essential to plan imaging tasks for large regional coverage using multiple satellites. First, we establish a 0-1 integer programming model to accurately describe the problem and analyze the challenges associated with solving the model. Second, we propose a heuristic algorithm based on the triple grids method. This approach utilizes a generated grid to create fewer candidate strips, a calculation grid to determine the effective coverage area more accurately, and a refined grid to solve the issue of repeated coverage of strips. Furthermore, we employ an approximation algorithm to further improve the solutions obtained from the heuristic algorithm. By comparing the proposed method to the traditional greedy heuristic algorithm and three evolutionary algorithms, the results show that our method has better performance in terms of coverage and efficiency.
For a given urban area, we apply the existing bus-based ad hoc networks (BANETs) to collect and transmit information, monitored by wireless sensor networks (WSNs), from subareas to the data center. Sensors are well de...
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For a given urban area, we apply the existing bus-based ad hoc networks (BANETs) to collect and transmit information, monitored by wireless sensor networks (WSNs), from subareas to the data center. Sensors are well deployed in each subareas divided by streets. WSNs and BANETs are heterogeneous and minimal gateways are required to connect the both kinds of networks. In this paper, we provide two gateway placement problems" minimum gateways placement and minimal gateways placement with minimum average delay. We present two constant algorithm MGPPA and MADGPPA to solve the two problems, respectively. Theoretical analysis demonstrates that MGPPA is a (1 + In lambda)-approximation algorithm and MADGPPA is a lambda-approximation algorithm correspondingly, where lambda is the maximum number of subareas covered by a gateway candidate. In the geometric topology of the grid urban area, lambda <= 4. Extensive comparison simulation show the performance of minimum gateways and minimal gateways with minimum average delay achieves significantly.
In wireless communication, the signal of a typical broadcast station is transmitted from a broadcast center p and reaches objects at a distance, say, r from it. In addition there is a radius r 0 , r 0 < r, such tha...
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In wireless communication, the signal of a typical broadcast station is transmitted from a broadcast center p and reaches objects at a distance, say, r from it. In addition there is a radius r 0 , r 0 < r, such that the signal originating from the center of the station is so strong that human habitation within distance r 0 from the center p should be avoided. In other words, points within distance r 0 from the station comprise a hazardous zone. We consider the following station layout proble: Cover a given planar region that includes a collection of buildings with a minimum number of stations so that every point in the region is within the reach of a station, while at the same time no interior point of any building is within the hazardous zone of a station. We give algorithms for computing such station layouts in both the one- and two-dimensional cases.
Generating explanations for graph neural networks (GNNs) has been studied to understand their behaviors in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GN...
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Generating explanations for graph neural networks (GNNs) has been studied to understand their behaviors in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable. We propose GVEX, a novel paradigm that generates Graph Views for GNN EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is Σ2P-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4-approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX.
The input to a PPNC instance is integers n and p , and a non-negative real weighting of the edges of the clique K n on the vertex set {1,..., n } . We are asked to find a set of p disjoint cycles spanning {1,..., n } ...
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The input to a PPNC instance is integers n and p , and a non-negative real weighting of the edges of the clique K n on the vertex set {1,..., n } . We are asked to find a set of p disjoint cycles spanning {1,..., n } and subject to this such that the sum of the weights of the edges is minimized. We provide an efficient approximation algorithm for the metric version of this problem which has an approximation ratio of 4 if p ≤ n/5 and an approximation ratio of 51 for larger p . For p > n/5, our algorithm uses a subroutine which approximately solves the Mod 3 T -join With Slack problem. The input to an instance of Mod k T -join with Slack consists of integers n and B , a non-negative weighting of the edges of the clique K n , and a label l(v) from {0,1,..., k - 1} on each vertex of K n . We are asked to find the minimum weight spanning forest F from amongst those satisfying ∑ T∈F ((∑ v∈V(T) l(v)) mod k ) ≤ B . If k = 2 and B = 0 this is the well-studied T -join problem which can be solved exactly in polynomial time.
A critical issue in battery-powered sensor networks is to construct energy efficient virtual backbones for network routing. Recent study in battery technology reveals that batteries tend to discharge more power than n...
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A critical issue in battery-powered sensor networks is to construct energy efficient virtual backbones for network routing. Recent study in battery technology reveals that batteries tend to discharge more power than needed and reimburse the over-discharged power if they are recovered. In this paper we first provide a mathematical battery model suitable for implementation in sensor networks. We then introduce the concept of battery-aware connected dominating set (BACDS) and show that in general the minimum BACDS (MBACDS) can achieve longer lifetime than the previous backbone structures. Then we show that finding a MBACDS is NP-hard and give a distributed approximation algorithm to construct the BACDS. The resulting BACDS constructed by our algorithm is at most (8+Delta) opt size, where. is the maximum node degree and opt is the size of an optimal BACDS. Simulation results show that the BACDS can save a significant amount of energy and achieve up to 30% longer network lifetime than previous schemes.
The intensity of radio waves decays rapidly with increasing propagation distance, and an edge server's antenna needs more power to form a larger signal coverage area. Therefore, the power of the edge server should...
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The intensity of radio waves decays rapidly with increasing propagation distance, and an edge server's antenna needs more power to form a larger signal coverage area. Therefore, the power of the edge server should be controlled to reduce energy consumption. In addition, edge servers with capacitated resources provide services for only a limited number of users to ensure the quality of service (QoS). We set the signal transmission power for the antenna of each edge server and formed a signal disk, ensuring that all users were covered by the edge server signal and minimizing the total power of the system. This scenario is a typical geometric set covering problem, and even simple cases without capacity limits are NP-hard problems. In this paper, we propose a primal-dual-based algorithm and obtain an m-approximation result. We compare our algorithm with two other algorithms through simulation experiments. The results show that our algorithm obtains a result close to the optimal value in polynomial time.
We present an exponential-time algorithm approximating the minimal lookahead necessary to win an omega-regular delay game. (c) 2022 Elsevier B.V. All rights reserved.
We present an exponential-time algorithm approximating the minimal lookahead necessary to win an omega-regular delay game. (c) 2022 Elsevier B.V. All rights reserved.
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