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Combinatorial network optimization with unknown variables: Multiarmed bandits with linear rewards and individual observations
 IEEE/ACM Transactions on Networking (TON
"... Abstract—We formulate the following combinatorial multiarmed bandit (MAB) problem: There are random variables with unknown mean that are each instantiated in an i.i.d. fashion over time. At each time multiple random variables can be selected, subject to an arbitrary constraint on weights associated ..."
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Cited by 37 (4 self)
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Abstract—We formulate the following combinatorial multiarmed bandit (MAB) problem: There are random variables with unknown mean that are each instantiated in an i.i.d. fashion over time. At each time multiple random variables can be selected, subject to an arbitrary constraint on weights associated with the selected variables. All of the selected individual random variables are observed at that time, and a linearly weighted combination of these selected variables is yielded as the reward. The goal is to find a policy that minimizes regret, defined as the difference between the reward obtained by a genie that knows the mean of each random variable, and that obtained by the given policy. This formulation is broadly applicable and useful for stochastic online versions of many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weighted matching,
A fast distributed approximation algorithm for minimum spanning trees
 IN PROCEEDINGS OF THE 20TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2006
"... We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our ..."
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Cited by 36 (8 self)
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We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exists graphs which need Ω(D(G) + L(G, w)) time to compute an Happroximation to the MST for any H ∈ [1, Θ(log n)]. Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the timeoptimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimal Õ(D(G)) time.
Improved Algorithms for Latency Minimization in Wireless Networks
 IN PROC. 36TH INTL. COLL. ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP
, 2009
"... In the interference scheduling problem, one is given a set of n communication requests described by sourcedestination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color clas ..."
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Cited by 34 (9 self)
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In the interference scheduling problem, one is given a set of n communication requests described by sourcedestination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class 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. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We introduce an instancebased measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of Ω(I/(log ∆ log n)) steps, where ∆ denotes the aspect ratio of the metric. When restricting to the twodimensional Euclidean space (as previous work) the bound improves to Ω(I / log ∆). Alternatively, when restricting to linear power assignments, the lower bound improves even to Ω(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only
Multihop local pooling for distributed throughput maximization in wireless networks
 in IEEE INFOCOM
, 2008
"... Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operatio ..."
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Cited by 31 (5 self)
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Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100 % throughput. However, previous work conditions and on networks with singlehop interference or singlehop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100 % of this throughput. Regarding multihop traffic, we show that if the network satisfies only the singlehop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100 % throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.
Supplement for Joint Congestion Control and Distributed Scheduling for Throughput Guarantees in Wireless Networks
, 2009
"... We consider the problem of throughputoptimal crosslayer design of wireless networks. We propose a joint congestion control and scheduling algorithm that achieves a fraction 1/dI(G) of the capacity region, where dI(G) depends on certain structural properties of the underlying connectivity graph G o ..."
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Cited by 25 (3 self)
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We consider the problem of throughputoptimal crosslayer design of wireless networks. We propose a joint congestion control and scheduling algorithm that achieves a fraction 1/dI(G) of the capacity region, where dI(G) depends on certain structural properties of the underlying connectivity graph G of the wireless network, and also on the type of interference constraints. For a wide range of wireless networks, dI(G) can be upper bounded by a constant, independent of the number of nodes in the network. The scheduling element of our algorithm is the maximal scheduling policy. Although this scheduling policy has been considered in several previous works, the challenges underlying its practical implementation in a fully distributed manner while accounting for necessary message exchanges have not been addressed in the literature. In this paper, we propose two algorithms for the distributed implementation of the maximal scheduling policy accounting for message exchanges, and analytically show that they still can achieve the performance guarantee under the 1hop and 2hop interference models. We also evaluate the performance of our crosslayer solutions in more realistic network settings with imperfect synchronization under the signaltointerferenceplusnoise ratio (SINR) interference model, and compare with the standard layered approaches such as TCP over IEEE 802.11b DCF networks.
Approximation algorithms for secondary spectrum auctions
 In Proc. 23rd Symp. Parallelism in Algorithms and Architectures (SPAA
, 2011
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Delay analysis for multihop wireless networks
 IEEE INFOCOM
, 2009
"... Abstract—We analyze the delay performance of a multihop wireless network with a fixed route between each sourcedestination pair. There are arbitrary interference constraints on the set of links that can be served simultaneously at any given time. These interference constraints impose a fundamental l ..."
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Cited by 21 (2 self)
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Abstract—We analyze the delay performance of a multihop wireless network with a fixed route between each sourcedestination pair. There are arbitrary interference constraints on the set of links that can be served simultaneously at any given time. These interference constraints impose a fundamental lower bound on the delay performance of any scheduling policy for the system. We present a methodology to derive such lower bounds. For the tandem queue network, where the delay optimal policy is known, the expected delay of the optimal policy numerically coincides with the lower bound. We conduct extensive numerical studies to suggest that the average delay of the backpressure scheduling policy can be made close to the lower bound by using appropriate functions of queue length. I.
Toward tractable computation of the capacity of multihop wireless networks
 IEEE INFOCOM 2007 PROCEEDINGS
, 2007
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Physical Interference Modeling for Transmission Scheduling on Commodity WiFi Hardware”, submitted for publication. (available at http://www.wings.cs.sunysb.edu/pubs/wifimodeling.pdf
"... Abstract—The demand for capacity in WiFi networks is driving a new look at transmission scheduling based link layers, particularly in the context of mesh networks. One basic issue here is the use of accurate interference models to drive transmission scheduling algorithms. However, experimental work ..."
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Cited by 13 (1 self)
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Abstract—The demand for capacity in WiFi networks is driving a new look at transmission scheduling based link layers, particularly in the context of mesh networks. One basic issue here is the use of accurate interference models to drive transmission scheduling algorithms. However, experimental work in this space has been limited. In this work, we use commodity WiFi hardware (specifically, 802.11a) for a comprehensive study on interference modeling for transmission scheduling on a mesh setup. We focus on the wellknown physical interference model for its realism. We empirically build the physical interference model via a packet reception rate vs. SINR relationship using a measurement driven method. We propose use of the “graded ” version of the model where feasibility of a link is probabilistic, as opposed to using the more traditional “thresholded ” version, where feasibility is binary. We show experimentally that the graded model is significantly more accurate (80 percentile error 0.2 vs. 0.55 for thresholded model). However, the graded model has never been considered in algorithmic studies on transmission scheduling. Carrying on further, we develop transmission scheduling experiments using greedy scheduling algorithms for the evacuation model for both interference models. We also develop similar experiments for optimal scheduling performance for the simplified oneshot scheduling. The scheduling experiments demonstrate clearly superior performance for the graded model, often by a factor of 2. I.
Online Capacity Maximization in Wireless Networks ∗
"... In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm n ..."
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Cited by 13 (4 self)
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In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the channel. Accepted requests must satisfy constraints on the signaltointerferenceplusnoise (SINR) ratio. The objective is to maximize the number of accepted requests. Using competitive analysis we study algorithms using distancebased power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1, ∆] and duration in [1, Γ] we derive a lower bound of Ω(Γ · ∆ d/2) on the competitive ratio of any deterministic online algorithm using a distancebased power assignment. Our main“ result is a nearoptimal deterministic algorithm that is O Γ · ∆ (d/2)+εcompetitive, for any constant ε> 0. Our algorithm for a single channel can be generalized to k channels. “ It can be adjusted to yield a competitive ratio of O k · Γ 1/k′ · ∆ (d/2k′ ′ ”