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55
Balanced graph partitioning
 In 16th Annual ACM Symposium on Parallelism in Algorithms and Architectures
, 2004
"... We consider the problem of partitioning a graph into k components of roughly equal size while minimizing the capacity of the edges between different components of the cut. In particular we require that for a parameter ν ≥ 1, no component contains more than ν · n k of the graph vertices. For k = 2 an ..."
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Cited by 67 (0 self)
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We consider the problem of partitioning a graph into k components of roughly equal size while minimizing the capacity of the edges between different components of the cut. In particular we require that for a parameter ν ≥ 1, no component contains more than ν · n k of the graph vertices. For k = 2 and ν = 1 this problem is equivalent to the well known Minimum Bisection Problem for which an approximation algorithm with a polylogarithmic approximation guarantee has been presented in [FK02]. For arbitrary k and ν ≥ 2 a bicriteria approximation ratio of O(logn) was obtained by [ENRS99] using the spreading metrics technique. We present a bicriteria approximation algorithm that for any constant ν> 1 runs in polynomial time and guarantees an approximation ratio of O(log1.5 n) (for a precise statement of the main result see Theorem 6). For ν = 1 and k ≥ 3 we show that no polynomial time approximation algorithm can guarantee a finite approximation ratio unless P = NP. 1
Adaptive Packet Routing for Bursty Adversarial Traffic
, 1998
"... One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separatio ..."
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Cited by 65 (8 self)
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One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separation has a serious drawback: each packet's path is fixed at the source and cannot be modified adaptively enroute. The problem is especially severe when packet injections are modeled by an adversary, whose goal is to cause "trafficjams".
Asymptotically optimal algorithm for job shop scheduling and packet routing
 J. Algorithms
, 1999
"... We propose asymptotically optimal algorithms for the job shop scheduling and packet routing problems. We propose a fluid relaxation for the job shop scheduling problem in which we replace discrete jobs with the flow of a continuous fluid. We compute an optimal solution of the fluid relaxation in clo ..."
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Cited by 64 (3 self)
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We propose asymptotically optimal algorithms for the job shop scheduling and packet routing problems. We propose a fluid relaxation for the job shop scheduling problem in which we replace discrete jobs with the flow of a continuous fluid. We compute an optimal solution of the fluid relaxation in closed form, obtain a lower bound Cmax to the job shop scheduling problem, and construct a feasible schedule from the fluid relaxation with objective value at most C � OŽ C. max ' max, where the constant in the OŽ. � notation is independent of the number of jobs, but it depends on the processing time of the jobs, thus producing an asymptotically optimal schedule as the total number of jobs tends to infinity. If the initially present jobs increase proportionally, then our algorithm produces a schedule with value at most C � OŽ. max 1. For the packet routing problem with fixed paths the previous algorithm applies directly. For the general packet routing problem we propose a linear programming relaxation that provides a lower bound Cmax and an asymptotically optimal algorithm that uses the optimal solution of the relaxation with objective value at most C � OŽ C. max ' max. Unlike asymptotically optimal algorithms that rely on probabilistic assumptions, our proposed algorithms make no probabilistic assumptions and they are asymptotically optimal for all instances with a large number of jobs Ž packets.. In computational experiments our algorithms produce schedules which are within 1 % of optimality even for moderately sized problems.
Message Multicasting In Heterogeneous Networks
, 1998
"... In heterogeneous networks, sending messages may incur different delays on different links, and each node may have a different switching time between messages. The well studied Telephone model is obtained when all link delays and switching times are equal to one unit. We investigate the problem of fi ..."
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Cited by 53 (0 self)
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In heterogeneous networks, sending messages may incur different delays on different links, and each node may have a different switching time between messages. The well studied Telephone model is obtained when all link delays and switching times are equal to one unit. We investigate the problem of finding the minimum time required to multicast a message from one source to a subset of the nodes of size k. The problem is NPhard even in the basic Telephone model. We present a polynomial time algorithm that approximates the minimum multicast time within a factor of O(log k). Our algorithm improves on the best known approximation factor for the Telephone model by a factor of O log n log log k . No approximation algorithms were known for the general model considered in this paper.
Stability of Adaptive and NonAdaptive Packet Routing Policies in Adversarial Queueing Networks
 In Proc. of the 31st STOC
, 2000
"... We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also ..."
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Cited by 46 (4 self)
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We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also propose a simple and distributed policy which is stable in an arbitrary adversarial queueing network even for the critical value of the arrival rate r = 1. Finally, a simple and checkable network flow type load condition is formulated for adaptive adversarial queueing networks and a policy is proposed which achieves stability under this new load condition. This load condition is a relaxation of the integral network flow type condition considered previously in the literature.
The Access Network Design Problem
, 1998
"... We consider the problem of designing a minimum costaccess network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types areavailable for leasing or buying. Some trunktypes have a high initial overhead cost but a low cost per unit bandwidth. Others have a ..."
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Cited by 45 (1 self)
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We consider the problem of designing a minimum costaccess network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types areavailable for leasing or buying. Some trunktypes have a high initial overhead cost but a low cost per unit bandwidth. Others have a low overhead cost but a high cost per unit bandwidth. When the central core is given, we show how to construct an access network whose cost is within O(KÂ²) of optimal,under weak assumptions on the cost structure. In contrast with previous bounds, this bound is independent of the network and the traffic. Typically, the value of K is small.Our approach uses a linear programming relaxation and is motivated by a rounding technique of Shmoys, Tardos andAardal [15]. Our techniques extend to a more complex situation inwhich the core is not given a priori. In this case we aim to minimize the switch cost of the core in addition to the trunkcost of the access network. We provide the same performance bound.
CrossLayer Latency Minimization in Wireless Networks with SINR Constraints
 MOBIHOC’07, SEPTEMBER 9–14, 2007, MONTREAL, QUEBEC, CANADA
, 2007
"... Recently, there has been substantial interest in the design of cross
layer protocols for wireless networks. These protocols optimize
certain performance metric(s) of interest (e.g. latency, energy, rate)
by jointly optimizing the performance of multiple layers of the
protocol stack. Algorithm desig ..."
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Cited by 41 (2 self)
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Recently, there has been substantial interest in the design of cross
layer protocols for wireless networks. These protocols optimize
certain performance metric(s) of interest (e.g. latency, energy, rate)
by jointly optimizing the performance of multiple layers of the
protocol stack. Algorithm designers often use geometricgraph
theoretic models for radio interference to design such crosslayer
protocols. In this paper we study the problem of designing cross
layer protocols for multihop wireless networks using a more real
istic Signal to Interference plus Noise Ratio (SINR) model for radio
interference. The following crosslayer latency minimization prob
lem is studied: Given a set V of transceivers, and a set of source
destination pairs, (i) choose power levels for all the transceivers, (ii)
choose routes for all connections, and (iii) construct an endtoend
schedule such that the SINR constraints are satisfied at each time
step so as to minimize the makespan of the schedule (the time
by which all packets have reached their respective destinations).
We present a polynomialtime algorithm with provable worstcase
performance guarantee for this crosslayer latency minimization
problem. As corollaries of the algorithmic technique we show that
a number of variants of the crosslayer latency minimization prob
lem can also be approximated efficiently in polynomial time. Our
work extends the results of Kumar et al. (Proc. SODA, 2004) and
Moscibroda et al. (Proc. MOBIHOC, 2006). Although our algo
rithm considers multiple layers of the protocol stack, it can natu
rally be viewed as compositions of tasks specific to each layer —
this allows us to improve the overall performance while preserving
the modularity of the layered structure.
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
Designing overlay multicast networks for streaming
 In Proceedings of ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that ..."
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Cited by 25 (6 self)
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In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.