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Simple Approximation Algorithms and PTASs for Various Problems in Wireless Ad Hoc Networks
, 2005
"... A wireless ad hoc network is often composed of a set V of n wireless devices distributed in a twodimensional domain. For each wireless device (also called node) u ∈ V, there is a transmission region within which signaltonoiseratio (SNR) is at least a threshold γ so that the signal transmitted by ..."
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Cited by 9 (6 self)
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A wireless ad hoc network is often composed of a set V of n wireless devices distributed in a twodimensional domain. For each wireless device (also called node) u ∈ V, there is a transmission region within which signaltonoiseratio (SNR) is at least a threshold γ so that the signal transmitted by u can be correctly received by other nodes with high probability. The transmission region is often modeled as a disk centered at the node u. In addition, for each node u, there is an interference region within which the transmission from u makes the signaltointerferenceandnoiseratio (SINR) of the legitimate receiver smaller than the threshold γ so that the legitimate receiver cannot correctly receive the message from the legitimate transmitter. In this paper, we first present new graph models to model the communication graphs and the interference graphs defined by wireless ad hoc networks with attention to interferencefree channel assignment or scheduling. Then we propose some simple approximation algorithms and/or PTASs (polynomial time approximation scheme) to approximate several classical graph problems such as maximum independent set, minimum vertex cover and minimum vertex coloring in these graph models. In addition, we also discuss various possible applications for these simple approximation algorithms and/or PTASs in wireless ad hoc networks.
Theoretically Good Distributed CDMA/OVSF Code Assignment for Wireless Ad Hoc Networks
 Tech Report, IIT, 2004, http://www.cs.iit.edu/∼xli/publicationsselect.htm XiangYang Li and PengJun Wan
"... Abstract. We present several distributed CDMA/OVSF code assignment algorithms for wireless ad hoc networks modelled by unit disk graph (UDG). We first give a distributed code assignment whose total throughput is within a constant factor of the optimum. Then we give a distributed method such that the ..."
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Abstract. We present several distributed CDMA/OVSF code assignment algorithms for wireless ad hoc networks modelled by unit disk graph (UDG). We first give a distributed code assignment whose total throughput is within a constant factor of the optimum. Then we give a distributed method such that the minimum rate achieved is within a constant factor of the optimum. A distributed method that can approximate both the minimum rate and total throughput is also presented. All our methods use only O(n) total messages (each with O(log n) bits)for an ad hoc wireless network of n nodes modelled by UDG.
ConstantCompetitive Algorithms for Online OVSF Code Assignment. manuscript
"... Orthogonal Variable Spreading Factor (OVSF) code assignment is a fundamental problem in Wideband CodeDivision MultipleAccess (WCDMA) systems, which plays an important role in third generation mobile communications. In the OVSF problem, codes must be assigned to incoming call requests with differe ..."
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Cited by 3 (2 self)
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Orthogonal Variable Spreading Factor (OVSF) code assignment is a fundamental problem in Wideband CodeDivision MultipleAccess (WCDMA) systems, which plays an important role in third generation mobile communications. In the OVSF problem, codes must be assigned to incoming call requests with different data rate requirements, in such a way that they are mutually orthogonal with respect to an OVSF code tree. An OVSF code tree is a complete binary tree in which each node represents a code associated with the combined bandwidths of its two children. To be mutually orthogonal, each leaftoroot path must contain at most one assigned code. In this paper, we focus on the online version of the OVSF code assignment problem and give a 10competitive algorithm, improving the previous O(h)competitive result, where h is the height of the code tree, and also another recent constantcompetitive result, where the competitive ratio is only constant under amortized analysis and the constant is never determined. Finally, we also improve the lower bound of the problem from 3/2 to 5/3. 1
Online Tree Node Assignment with Resource Augmentation
"... Abstract. Given a complete binary tree of height h,theonline tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, withanintegerparameter0 ≤ i ≤ h, is served by assigning a (tree) node at level (or height) i and a release request is served b ..."
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Abstract. Given a complete binary tree of height h,theonline tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, withanintegerparameter0 ≤ i ≤ h, is served by assigning a (tree) node at level (or height) i and a release request is served by releasing a specified assigned node. The node assignments have to guarantee that no node is assigned to two assignment requests unreleased, and every leaftoroot path of the tree contains at most one assigned node. With assigned node reassignments allowed, the target of the problem is to minimize the number of assignments/reassigments, i.e., the cost, to serve the whole sequence of requests. This online tree node assignment problem is fundamental to many applications, including OVSF code assignment in WCDMA networks, buddy memory allocation and hypercube subcube allocation. Most of the previous results focus on how to achieve good performance when the same amount of resource is given to both the online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online algorithm is allowed to use more trees than the optimal offline algorithm. By using different approaches, we give (1) a 1competitive online algorithm, which uses (h +1)/2 trees, and is optimal because (h +1)/2 trees are required by any online algorithm to match the cost of the optimal offline algorithm with one tree; (2) a 2competitive algorithm with 3h/8 + 2 trees; (3) an amortized (4/3 +α)competitive algorithm with (11/4 +4/(3α)) trees, for any α where 0 <α ≤ 4/3. 1
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, 2005
"... Simple approximation algorithms and PTASs for various problems in wireless ad hoc networks ..."
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Simple approximation algorithms and PTASs for various problems in wireless ad hoc networks
Theoretically Good Distributed CDMA/OVSF Code Assignment for Wireless Ad Hoc Networks
"... Orthogonal Variable Spreading Factor (OVSF) CDMA code has the ability to support higher and variable data rates with a single code using one transceiver. A number of CDMA code assignment algorithms have been developed and studied for cellular wireless networks, however, little is known about the ad ..."
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Orthogonal Variable Spreading Factor (OVSF) CDMA code has the ability to support higher and variable data rates with a single code using one transceiver. A number of CDMA code assignment algorithms have been developed and studied for cellular wireless networks, however, little is known about the ad hoc wireless networks. In this paper, we propose several distributed CDMA/OVSF code assignment algorithms for wireless ad hoc networks modelled by unit disk graph (UDG). We first study how to assign CDMA/OVSF code such that the total throughput achieved is within a constant factor of the optimum. Then we give a distributed method such that the minimum rate achieved is within a constant factor of the minimum rate of any valid code assignment. A distributed method that can approximate both the minimum rate and total throughput is also presented. Finally, we present a post processing method to further improve these code assignments. All our methods use only O(n) total messages (each with O(log n) bits) for an ad hoc wireless network of n devices modelled by UDG.