scispace - formally typeset
Search or ask a question
Proceedings ArticleDOI

Approximation Algorithms for Computing Capacity of Wireless Networks with SINR Constraints

TL;DR: This paper develops polynomial time algorithms to provably approximate the total throughput in this setting of the capacity estimation problem using the more general Signal to Interference Plus Noise Ratio model for interference, on arbitrary wireless networks.
Abstract: A fundamental problem in wireless networks is to estimate its throughput capacity - given a set of wireless nodes, and a set of connections, what is the maximum rate at which data can be sent on these connections. Most of the research in this direction has focused on either random distributions of points, or has assumed simple graph-based models for wireless interference. In this paper, we study capacity estimation problem using the more general Signal to Interference Plus Noise Ratio (SINR) model for interference, on arbitrary wireless networks. The problem becomes much harder in this setting, because of the non-locality of the SINR model. Recent work by Moscibroda et al. (2006) has shown that the throughput in this model can differ from graph based models significantly. We develop polynomial time algorithms to provably approximate the total throughput in this setting.

Content maybe subject to copyright    Report

Citations
More filters
Proceedings ArticleDOI
19 Apr 2009
TL;DR: This work proposes the first scheduling algorithm with approximation guarantee independent of the topology of the network, and proves that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions.
Abstract: In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network's topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes.

296 citations


Cites background from "Approximation Algorithms for Comput..."

  • ...In [4], an algorithm with approximation guarantee of O(log Δ) was proposed, where Δ is the ratio between the maximum and the minimum distances between nodes....

    [...]

  • ...2 This problem was shown to be NP-complete in [9], and the few algorithms with provable approximation guarantee proposed so far yield arbitrarily bad performance, depending on the topology of the network [2], [4], [9] (see Related Work Section)....

    [...]

Proceedings ArticleDOI
19 Apr 2009
TL;DR: It is shown that maximizing the number of supported connections is NP-hard, even when there is no background noise, in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming.
Abstract: In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported). Our results are: ldr We show that maximizing the number of supported connections is NP-hard, even when there is no background noise. This is in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming. ldr We present a number of approximation algorithms for the problem. All of these approximation algorithms run in polynomial time and have an approximation ratio that is independent of the number of connections. ldr We examine a completely distributed algorithm and analyze it as a game in which a connection receives a positive payoff if it is successful and a negative payoff if it is unsuccessful while transmitting with nonzero power. We show that in this game there is not necessarily a pure Nash equilibrium but if such an equilibrium does exist the corresponding price of anarchy is independent of the number of connections. We also show that a mixed Nash equilibrium corresponds to a probabilistic transmission strategy and in this case such an equilibrium always exists and has a price of anarchy that is independent of the number of connections. This work was supported by NSF contract CCF-0728980 and was performed while the second author was visiting Bell Labs in Summer, 2008.

220 citations


Cites background from "Approximation Algorithms for Comput..."

  • ...Previous papers that consider the complexity of capacity maximization in the SINR model include [3], [5], [9], [15],...

    [...]

Book ChapterDOI
06 Jul 2009
TL;DR: The main result proves that wireless scheduling is in APX, and a robustness result is presented, showing that constant parameter and model changes will modify the result only by a constant.
Abstract: In this paper we address a common question in wireless communication: How long does it take to satisfy an arbitrary set of wireless communication requests? This problem is known as the wireless scheduling problem. Our main result proves that wireless scheduling is in APX. In addition we present a robustness result, showing that constant parameter and model changes will modify the result only by a constant.

168 citations


Additional excerpts

  • ...[6])....

    [...]

Proceedings ArticleDOI
10 Aug 2009
TL;DR: It is proved that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the interference scheduling problem, which is the worst possible performance guarantee as there is a straightforward algorithm that achieves an O(n)-approximation.
Abstract: In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated receiving device. In the bidirectional version the devices within a pair shall be able to exchange signals in both directions. In both versions, each pair must be assigned a power level and a color such that the pairs in each color class (representing pairs communicating in the same time slot) can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. This is commonly referred to as the "physical model" and is the established way of modelling interference in the engineering community. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests.We study oblivious power assignments in which the power value of a pair only depends on the distance between the points of this pair. We prove that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the problem, which is the worst possible performance guarantee as there is a straightforward algorithm that achieves an O(n)-approximation. For the bidirectional version, however, we can show the existence of a universally good oblivious power assignment: For any set of n bidirectional communication requests, the so-called "square root assignment" admits a coloring with at most polylog(n) times the minimal number of colors. The proof for the existence of this coloring is non-constructive. We complement it by an approximation algorithm for the coloring problem under the square root assignment. This way, we obtain the first polynomial time algorithm with approximation ratio polylog(n) for interference scheduling in the physical model.

123 citations


Cites background from "Approximation Algorithms for Comput..."

  • ...This implies that the loss in this class is in [4, 4)....

    [...]

  • ...The objective in [3] is to minimize the end-to-end latency, while [4] aims at maximizing throughput....

    [...]

  • ...However, these requests might violate the interference constraints with gain β because of the following reasons: a) We assumed that the loss in class Ci is exactly 4 −αi rather than from the interval [4, 4)....

    [...]

  • ...Some recent theoretical studies [12, 13, 3, 4] use a more realistic model, the so-called physical model, which is wellaccepted in the engineering community....

    [...]

  • ...[3, 4] study a multi-hop version of the interference scheduling problem on two-dimensional Euclidean instances, that is, they additionally consider the aspect of routing on top of the tasks power assignment and coloring....

    [...]

Proceedings ArticleDOI
10 Apr 2011
TL;DR: A unified algorithmic framework is built and approximation algorithms for link scheduling with or without power control are developed for maximizing throughput capacity or minimizing the communication latency in multihop wireless networks under the physical interference model.
Abstract: Link scheduling is a fundamental problem in multihop wireless networks because the capacities of the communication links in multihop wireless networks, rather than being fixed, vary with the underlying link schedule subject to the wireless interference constraint. The majority of algorithmic works on link scheduling in multihop wireless networks assume binary interference models such as the 802.11 interference model and the protocol interference model, which often put severe restrictions on interference constraints for practical applicability of the link schedules. On the other hand, while the physical interference model is much more realistic, the link scheduling problem under physical interference model is notoriously hard to resolve and been studied only recently by a few works. This paper conducts a full-scale algorithmic study of link scheduling for maximizing throughput capacity or minimizing the communication latency in multihop wireless networks under the physical interference model. We build a unified algorithmic framework and develop approximation algorithms for link scheduling with or without power control.

103 citations

References
More filters
Journal ArticleDOI
TL;DR: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits persecond under a noninterference protocol.
Abstract: When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.

9,008 citations

Proceedings ArticleDOI
14 Sep 2003
TL;DR: It is shown that the routes derived from the analysis often yield noticeably better throughput than the default shortest path routes even in the presence of uncoordinated packet transmissions and MAC contention, suggesting that there is opportunity for achieving throughput gains by employing an interference-aware routing protocol.
Abstract: In this paper, we address the following question: given a specific placement of wireless nodes in physical space and a specific traffic workload, what is the maximum throughput that can be supported by the resulting network? Unlike previous work that has focused on computing asymptotic performance bounds under assumptions of homogeneity or randomness in the network topology and/or workload, we work with any given network and workload specified as inputs.A key issue impacting performance is wireless interference between neighboring nodes. We model such interference using a conflict graph, and present methods for computing upper and lower bounds on the optimal throughput for the given network and workload. To compute these bounds, we assume that packet transmissions at the individual nodes can be finely controlled and carefully scheduled by an omniscient and omnipotent central entity, which is unrealistic. Nevertheless, using ns-2 simulations, we show that the routes derived from our analysis often yield noticeably better throughput than the default shortest path routes even in the presence of uncoordinated packet transmissions and MAC contention. This suggests that there is opportunity for achieving throughput gains by employing an interference-aware routing protocol.

1,828 citations


"Approximation Algorithms for Comput..." refers background in this paper

  • ...The vectors f̄ and x̄ are called the flow vector and link utilization vector respectively....

    [...]

  • ...The algorithmic aspects of network capacity have been studied in a number of papers, such as [2], [9]–[11], [13], [20]....

    [...]

Proceedings ArticleDOI
28 Aug 2005
TL;DR: A solution is developed that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients, and the performance of the algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem.
Abstract: Multi-hop infrastructure wireless mesh networks offer increased reliability, coverage and reduced equipment costs over their single-hop counterpart, wireless LANs. Equipping wireless routers with multiple radios further improves the capacity by transmitting over multiple radios simultaneously using orthogonal channels. Efficient channel assignment and routing is essential for throughput optimization of mesh clients. Efficient channel assignment schemes can greatly relieve the interference effect of close-by transmissions; effective routing schemes can alleviate potential congestion on any gateways to the Internet, thereby improving per-client throughput. Unlike previous heuristic approaches, we mathematically formulate the joint channel assignment and routing problem, taking into account the interference constraints, the number of channels in the network and the number of radios available at each mesh router. We then use this formulation to develop a solution for our problem that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients. We show that the performance of our algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem. Our evaluation demonstrates that our algorithm can effectively exploit the increased number of channels and radios, and it performs much better than the theoretical worst case bounds.

1,154 citations

Proceedings ArticleDOI
28 Aug 2005
TL;DR: This paper provides necessary conditions to verify the feasibility of rate vectors in next generation fixed wireless broadband networks, and uses them to derive upper bounds on the capacity in terms of achievable throughput, using a fast primal-dual algorithm.
Abstract: Next generation fixed wireless broadband networks are being increasingly deployed as mesh networks in order to provide and extend access to the internet. These networks are characterized by the use of multiple orthogonal channels and nodes with the ability to simultaneously communicate with many neighbors using multiple radios (interfaces) over orthogonal channels. Networks based on the IEEE 802.11a/b/g and 802.16 standards are examples of these systems. However, due to the limited number of available orthogonal channels, interference is still a factor in such networks. In this paper, we propose a network model that captures the key practical aspects of such systems and characterize the constraints binding their behavior. We provide necessary conditions to verify the feasibility of rate vectors in these networks, and use them to derive upper bounds on the capacity in terms of achievable throughput, using a fast primal-dual algorithm. We then develop two link channel assignment schemes, one static and the other dynamic, in order to derive lower bounds on the achievable throughput. We demonstrate through simulations that the dynamic link channel assignment scheme performs close to optimal on the average, while the static link channel assignment algorithm also performs very well. The methods proposed in this paper can be a valuable tool for network designers in planning network deployment and for optimizing different performance objectives.

825 citations


"Approximation Algorithms for Comput..." refers background in this paper

  • ...The algorithmic aspects of network capacity have been studied in a number of papers, such as [2], [9]–[11], [13], [20]....

    [...]

Journal ArticleDOI
TL;DR: A solution is developed that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients, and the performance of the algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem.
Abstract: Multihop infrastructure wireless mesh networks offer increased reliability, coverage, and reduced equipment costs over their single-hop counterpart, wireless local area networks. Equipping wireless routers with multiple radios further improves the capacity by transmitting over multiple radios simultaneously using orthogonal channels. Efficient channel assignment and routing is essential for throughput optimization of mesh clients. Efficient channel assignment schemes can greatly relieve the interference effect of close-by transmissions; effective routing schemes can alleviate potential congestion on any gateways to the Internet, thereby improving per-client throughput. Unlike previous heuristic approaches, we mathematically formulate the joint channel assignment and routing problem, taking into account the interference constraints, the number of channels in the network, and the number of radios available at each mesh router. We then use this formulation to develop a solution for our problem that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients. We show that the performance of our algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem. Our evaluation demonstrates that our algorithm can effectively exploit the increased number of channels and radios, and it performs much better than the theoretical worst case bounds

679 citations


"Approximation Algorithms for Comput..." refers background in this paper

  • ...The algorithmic aspects of network capacity have been studied in a number of papers, such as [2], [9]–[11], [13], [20]....

    [...]