In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, ...
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ISBN:
(纸本)9783030247669;9783030247652
In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.4 - epsilon)-approximation algorithm requiring only a single pass through the data. This improves on the currently best (0.363 - epsilon)-approximation algorithm. The required memory space depends only on the size of the knapsack capacity and e.
Wireless Rechargeable Sensor Network (WRSN) becomes a hot research issue in recent years owing to the breakthrough of wireless power transfer technology. Most prior arts concentrate on developing scheduling schemes in...
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ISBN:
(纸本)9781728125190
Wireless Rechargeable Sensor Network (WRSN) becomes a hot research issue in recent years owing to the breakthrough of wireless power transfer technology. Most prior arts concentrate on developing scheduling schemes in 2-D networks where mobile chargers are placed on the ground. However, few of them are suitable for 3-D scenarios, making it difficult or even impossible to popularize in practical applications. In this paper, we focus on the problem of charging a 3-D WRSN with an Unmanned Aerial Vehicle (UAV) to maximize charged energy within energy constraints. To deal with the problem, we propose a spatial discretization scheme to obtain a finite feasible charging spot set for UAV in 3-D environment and a temporal discretization scheme to determine charging duration for each charging spot. Then, we transform the problem into a submodular maximization problem with routing constraints, and present a cost-efficient approximation algorithm with a provable approximation ratio of e-1/4e(1 - epsilon) to solve it. Lastly, extensive simulations and test-bed experiments show the superior performance of our algorithm.
Beacon-based time-of-flight indoor localization systems have shown great promise for applications ranging from indoor navigation to asset tracking. In large-scale deployments, a major practical challenge is detemiinin...
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ISBN:
(纸本)9781450369091
Beacon-based time-of-flight indoor localization systems have shown great promise for applications ranging from indoor navigation to asset tracking. In large-scale deployments, a major practical challenge is detemiining the placement of a minimal number of beacons that ensures full coverage- each point in the domain lets line-of-sight paths to enough beacons to uniquely localize itself. Three beacons with line-of-sight paths are always enough, but two beacons within line of sight may also work, given a favorable geometry. In this paper, we propose two beacon placement algorithms that leverage the floor plan geometry with provable theoretical guarantees. First, we present a greedy algorithm using properties of sub-modular functions to place O(OPT " ln rn) beacons, where m is the number of discrete location points in the region that need to be localized, and OPT is the size of the optimal solution. Second, we present a random sampling algorillim [ital. places O(OPT " log(OPT)) beacons While localizing all targets. We evaluate our algorithms on both real-world and randomly generated floor plans. Our algorithms place on an average 6- 23% and 12% fewer beacons in real-world topologies and nuldondy generated floor plans respectively, as compared to prior work. We also present a study where we ask users to attempt to place nodes manually and discover that even humans Owl are well versed on the coverage problem find it hard to balance the trade-off between the number of beacons and area localized.
In this paper we present approximation preserving reductions from the Budgeted and Generalized Maximum Coverage Problems to the Knapsack Problem with Conflict Graphs. The reductions are used to yield Polynomial Time A...
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In this paper we present approximation preserving reductions from the Budgeted and Generalized Maximum Coverage Problems to the Knapsack Problem with Conflict Graphs. The reductions are used to yield Polynomial Time approximation Schemes for special classes of instances of these problems. Using these approximation schemes, the existence of pseudo-polynomial algorithms are proven and, in more particular cases, these algorithms are shown to have polynomial time complexity. Moreover, the characteristics of the instances that admit these algorithms are analyzed.
We give a (2 + epsilon)-approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture on the approximability ...
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We give a (2 + epsilon)-approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture on the approximability of this scheduling problem (Skutella, 2016). (C) 2018 Elsevier B.V. All rights reserved.
The Malleable Parallel Task Scheduling problem (MPTS) is an extension of one of the most classic scheduling problems (P parallel to C-max). The only difference is that for MPTS, each task can be processed simultaneous...
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The Malleable Parallel Task Scheduling problem (MPTS) is an extension of one of the most classic scheduling problems (P parallel to C-max). The only difference is that for MPTS, each task can be processed simultaneously by more than one processor. Such flexibility could dramatically reduce the makespan, but greatly increase the difficulty for solving the problem. By carefully analyzing some existing algorithms for MPTS, we find each of them suitable for some specific cases, but none is effective enough for all cases. Based on such observations, we introduce some optimization algorithms and improving techniques for MPTS, with their performance analyzed in theory. Combining these optimization algorithms and improving techniques gives rise to our novel scheduling algorithm OCM (Optimizations Combined for MPTS), a 2-approximation algorithm for MPTS. Extensive simulations on random datasets and SPLASH-2 benchmark reveal that for all cases, schedules produced by OCM have smaller makespans, compared with other existing algorithms. (C) 2012 Elsevier Inc. All rights reserved.
In this paper, we study the dominating selection optimisation problem with multiple channels and multiple radios in wireless sensor networks. The objective is to maximise the number of targets covered while selecting ...
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In this paper, we study the dominating selection optimisation problem with multiple channels and multiple radios in wireless sensor networks. The objective is to maximise the number of targets covered while selecting at most k nodes and at most k(i) channels with each selected node v(i). Our problem is a general case of the maximum coverage problem. We propose two algorithms: the first one is based on linear programming and PIPAGE rounding, in which its approximation ratio is 1/K(1-(1-1/m)(m)), where m is the number of the dominating nodes and K = max k(i). The second algorithm is based on greedy strategy with low time complexity. The simulation shows that the both two algorithms have good performance.
We study the Betweenness problem. We are given a set of vertices and betweenness constraints. Each betweenness constraint of the form x similar to {y, z} requires that vertex x lies between vertices y and z. Our goal ...
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We study the Betweenness problem. We are given a set of vertices and betweenness constraints. Each betweenness constraint of the form x similar to {y, z} requires that vertex x lies between vertices y and z. Our goal is to find a vertex ordering that maximizes the number of satisfied constraints. In 1995, Chor and Sudan designed an SDP algorithm that satisfies half of all constraints in a satisfiable instance. We present a simple combinatorial linear time algorithm with the same approximation guarantee. (C) 2012 Elsevier B.V. All rights reserved.
Rapid penetration of renewable energy based Distributed Energy Resources (DER) has the potential to exacerbate the challenges inherent in grid frequency and voltage regulation. However, their real time controllability...
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ISBN:
(纸本)9781450366717
Rapid penetration of renewable energy based Distributed Energy Resources (DER) has the potential to exacerbate the challenges inherent in grid frequency and voltage regulation. However, their real time controllability can be leveraged to not only mitigate such challenges, but improve the economics and quality of grid operations. A plethora of DER scheduling algorithms have been developed for fast and efficient scheduling of these resources. These algorithms schedule the complex - real and reactive power injected into (or drawn from) the grid by the DERs under various cost objective functions and grid constraints. However, a vast majority of such algorithms assume the feasible range of power injections to be continuous. In reality, the control options available for several DERs form a discrete space. This implies that the feasible range of power injections also forms a discrete space. This makes DER scheduling an NP-hard problem. Integer/Mixed Integer program based algorithms, which guarantee optimality in the objective value, have been developed. But these are prohibitively expensive in terms of computational time requirements. On the other hand, fast heuristic based solutions have also been developed. But as they do not provide any guarantee on the optimality of the objective, or on satisfying the constraints, they are unreliable for grid operations. Recent works have developed approximation algorithms which offer the best of both the approaches above: (near) optimality and low computational complexity, both of which are governed by a user defined accuracy parameter.. In this work, we significantly improve upon such existing works by developing an approximation algorithm which schedules DERs with complex injections (as opposed to only real injection) and whose runtime is polynomial (as opposed to exponential) in 1/epsilon. We provide theoretical analysis and support them with experimental results to validate the guarantees provided by our approximation algorithm.
Given lambda > 0, an undirected complete graph G = (V, E) with nonnegative edge-weight function obeying the triangle inequality and a depot vertex r is an element of V, a set {C-1, ... , C-k} of cycles is called a ...
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ISBN:
(纸本)9783030261764;9783030261757
Given lambda > 0, an undirected complete graph G = (V, E) with nonnegative edge-weight function obeying the triangle inequality and a depot vertex r is an element of V, a set {C-1, ... , C-k} of cycles is called a lambda-bounded r-cycle cover if V subset of boolean OR(k)(i=1) V (C-i) and each cycle C-i contains r and has a length of at most lambda. The Distance Constrained Vehicle Routing Problem with the objective of minimizing the total cost (DVRP-TC) aims to find a lambda-bounded r-cycle cover {C-1, ... , C-k} such that the sum of the total length of the cycles and gamma k is minimized, where gamma is an input indicating the assignment cost of a single cycle. For DVRP-TC on tree metric, we show a 2-approximation algorithm that is implied by the existing results and give an LP relaxation whose integrality gap has an upper bound of 5/2. In particular, when gamma = 0 we prove that this bound can be improved to 2. For the unrooted version of DVRP-TC, we devise a 5-approximation algorithm and show that a natural set-covering LP relaxation has a constant integrality gap of 25 using the rounding procedure given by Nagarajan and Ravi (2008).
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