Results 1  10
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24
Improved approximation algorithms for broadcast scheduling
 In Proc. of 7 th Annual ACMSIAM Symposium on Discrete Algorithms
, 2004
"... We consider two scheduling problems in the broadcast setting. The first is that of minimizing the average response time of requests. For the offline version of this problem we give an algorithm with an approximation ratio of O(log 2 (n) / log log(n)), where n is the total number of pages. This subst ..."
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Cited by 30 (3 self)
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We consider two scheduling problems in the broadcast setting. The first is that of minimizing the average response time of requests. For the offline version of this problem we give an algorithm with an approximation ratio of O(log 2 (n) / log log(n)), where n is the total number of pages. This substantially improves the previously best known approximation factor of O ( √ n) for the problem [3]. Our second result is for the profit maximization version of the broadcast scheduling problem. Here each request has a deadline and a profit which is obtained if the request is satisfied before its deadline. The goal is to maximize the total profit. We give an algorithm with an approximation ratio of 5/6, which improves the previously best known approximation guarantee of 3/4 for the problem [13]. 1
Delay with network coding and feedback
 In ISIT’09: Proceedings of the 2009 IEEE international conference on Symposium on Information Theory
, 2009
"... Abstract—We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of µ messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages ..."
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Cited by 21 (0 self)
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Abstract—We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of µ messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by realtime applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Θ(µ) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NPhard when the sender only schedules single messages and that the general problem remains NPhard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations. I.
An Online Scalable Algorithm for Average Flowtime in Broadcast Scheduling
 In SODA 10: Proceedings of the twentyfirst annual ACMSIAM symposium on Discrete algorithms
, 2010
"... In this paper the online pullbased broadcast model is considered. In this model, there are n pages of data stored at a server and requests arrive for pages online. When the server broadcasts page p, all outstanding requests for the same page p are simultaneously satisfied. We consider the problem o ..."
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Cited by 16 (12 self)
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In this paper the online pullbased broadcast model is considered. In this model, there are n pages of data stored at a server and requests arrive for pages online. When the server broadcasts page p, all outstanding requests for the same page p are simultaneously satisfied. We consider the problem of minimizing average (total) flow time online where all pages are unitsized. For this problem, there has been a decadelong search for an online algorithm which is scalable, i.e. (1 + ɛ)speed O(1)competitive for any fixed ɛ> 0. In this paper, we give the first analysis of an online scalable algorithm. 1
Online scheduling to minimize the maximum delay factor
 IN SODA 09: PROCEEDINGS OF THE TWENTIETH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2009
"... In this paper two scheduling models are addressed. First is the standard model (unicast) where requests (or jobs) are independent. The other is the broadcast model where broadcasting a page can satisfy multiple outstanding requests for that page. We consider online scheduling of requests when they h ..."
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Cited by 12 (4 self)
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In this paper two scheduling models are addressed. First is the standard model (unicast) where requests (or jobs) are independent. The other is the broadcast model where broadcasting a page can satisfy multiple outstanding requests for that page. We consider online scheduling of requests when they have deadlines. Unlike previous models, which mainly consider the objective of maximizing throughput while respecting deadlines, here we focus on scheduling all the given requests with the goal of minimizing the maximum delay factor. The delay factor of a schedule is defined to be the minimum α ≥ 1 such that each request i is completed by time ai + α(di − ai) where ai is the arrival time of request i and di is its deadline. Delay factor generalizes the previously defined measure of maximum stretch which is based only the processing times of requests [9, 11]. We prove strong lower bounds on the achievable competitive ratios for delay factor scheduling even with unittime requests. Motivated by this, we consider resource augmentation analysis [24] and prove the following positive results. For the unicast model we give algorithms that are (1 + ɛ)speed O ( 1 ɛ)competitive in both the single machine and multiple machine settings. In the broadcast model we give an algorithm for samesized pages that is (2 + ɛ)speed O ( 1 ɛ 2)competitive. For arbitrary page sizes we give an algorithm that is (4 + ɛ)speed O ( 1 ɛ 2)competitive.
Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling
, 2009
"... We consider online algorithms for pullbased broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, name ..."
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Cited by 11 (7 self)
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We consider online algorithms for pullbased broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, namely maximum response time (waiting time) and maximum delayfactor and their weighted versions. We obtain the following results in the worstcase online competitive model. • We show that FIFO (firstin firstout) is 2competitive even when the page sizes are different. Previously this was known only for unitsized pages [10] via a delicate argument. Our proof differs from [10] and is perhaps more intuitive. • We give an online algorithm for maximum delayfactor that is O(1/ǫ 2)competitive with (1 + ǫ)speed for unitsized pages and with (2 + ǫ)speed for different sized pages. This improves on the algorithm in [12] which required (2+ǫ)speed and (4+ǫ)speed respectively. In addition we show that the algorithm and analysis can be extended to obtain the same results for maximum weighted response time and delay factor. • We show that a natural greedy algorithm modeled after LWF (LongestWaitFirst) is not O(1)competitive for maximum delay factor with any constant speed even in the setting of standard scheduling with unitsized jobs. This complements our upper bound and demonstrates the importance of the tradeoff made in our algorithm.
Longest wait first for broadcast scheduling
 IN WAOA ’09: PROCEEDINGS OF 7TH WORKSHOP ON APPROXIMATION AND ONLINE ALGORITHMS
, 2009
"... We consider online algorithms for broadcast scheduling. In the pullbased broadcast model there are n unitsized pages of information at a server and requests arrive online for pages. When the server transmits a page p, all outstanding requests for that page are satisfied. There is a lower bound of ..."
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Cited by 9 (6 self)
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We consider online algorithms for broadcast scheduling. In the pullbased broadcast model there are n unitsized pages of information at a server and requests arrive online for pages. When the server transmits a page p, all outstanding requests for that page are satisfied. There is a lower bound of Ω(n) on the competitiveness of online algorithms to minimize average flowtime [27]; therefore we consider resource augmentation analysis in which the online algorithm is given extra speed over the adversary. The longestwaitfirst (LWF) algorithm is a natural algorithm that has been shown to have good empirical performance [2]. Edmonds and Pruhs showed that LWF is 6speed O(1)competitive using a very complex analysis; they also showed that LWF is not O(1)competitive with less than 1.618speed. In this paper we make several contributions to the analysis of LWF and broadcast scheduling. – An intuitive and easy to understand analysis of LWF that shows that it is O(1/ɛ 2) competitive for average flowtime with 4+ɛ speed. – LWF is O(1/ɛ 3) competitive for average flowtime with 3.4+ɛ speed. We use our insights to prove that a natural extension of LWF is O(1)speed O(1) competitive for more general objective functions such as average delayfactor and Lk norms of delayfactor (for fixed k). These metrics generalize average flowtime and Lk norms of flowtime respectively and ours are the first nontrivial results for these objective functions.
A Model for Minimizing Active Processor Time
"... We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongas ..."
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Cited by 5 (3 self)
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We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongasit is “active”att. The goalis toschedule allthe jobs in the fewestnumber of active timeslots. The machine consumes a fixed amount of energy per active timeslot, regardless of the number of jobs scheduled in that slot (as long as the number of jobs is nonzero). In other words, subject to ℓi units of each job i being scheduled in its feasible region and at each slot at most B jobs being scheduled, we are interested in minimizing the total time during which the machine is active. We present a linear time algorithm for the case where jobs are unit length and each Ti is a single interval. For general Ti, we show that the problem is NPcomplete even for B = 3. However when B = 2, we show that it can be efficiently solved. In addition, we consider a version of the problem where jobs have arbitrary lengths and can be preempted at any point in time. For general B, the problem can be solved by linear programming. For B = 2, the problem amounts to finding a trianglefree 2matching on a special graph. We extend the algorithm of Babenko et. al. [5] to handle our variant, and also to handle nonunit length jobs. This yields an O ( √ Lm) time algorithm to solve the preemptive scheduling problem for B = 2, where L = ∑ iℓi. We alsoshow that for B = 2 and unit length jobs, the optimal nonpreemptive schedule has ≤ 4/3times the activetime of the optimal preemptive schedule; this bound extends to several versions of the problem when jobs have arbitrary length. 1
Online Scalable Scheduling for the ℓknorms of Flow Time Without Conservation of Work
"... We address the scheduling model of arbitrary speedup curves and the broadcast scheduling model. The former occurs when jobs are scheduled in a multicore system or on a cloud of machines. Here jobs can be sped up when given more processors or machines. However, the parallelizability of the jobs may ..."
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Cited by 4 (4 self)
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We address the scheduling model of arbitrary speedup curves and the broadcast scheduling model. The former occurs when jobs are scheduled in a multicore system or on a cloud of machines. Here jobs can be sped up when given more processors or machines. However, the parallelizability of the jobs may vary and the algorithm is required to be oblivious of the parallelizability of a job. The latter model is natural in wireless and LAN networks where requests (or jobs) can be simultaneously satisfied together. Both settings are similar in that two schedules can do different amounts of work to satisfy all the jobs. We focus on optimizing the ℓk norms of flow time. Recently, Gupta et al. [24] gave a (k + ɛ)speed O(1)competitive algorithm for the ℓk norms of flow time in both scheduling settings for fixed k. Inspired by this work, we give the first analysis of a scalable algorithm, i.e. (1 + ɛ)speed O(1)competitive, for all ℓknorms of flow time in both settings for fixed k and 0 < ɛ ≤ 1. Both problems have a strong lower bound without resource augmentation, so this is the best result that can be shown in the worst case setting up to a constant factor in the competitive ratio.
ONLINE SCHEDULING ALGORITHMS FOR AVERAGE FLOW TIME AND ITS VARIANTS
, 2012
"... This dissertation focuses on scheduling problems that are found in a clientserver setting where multiple clients and one server (or multiple servers) are the participating entities. Clients send their requests to the server(s) over time, and the server needs to satisfy the requests using its resour ..."
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Cited by 3 (2 self)
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This dissertation focuses on scheduling problems that are found in a clientserver setting where multiple clients and one server (or multiple servers) are the participating entities. Clients send their requests to the server(s) over time, and the server needs to satisfy the requests using its resources. This setting is prevalent in many applications including multiuser operating systems, web servers, database servers, and so on. A natural objective for each client is to minimize the flow time (or equivalently response time) of her request, which is defined as its completion time minus its release time. The server, with multiple requests to serve in its queue, has to prioritize the requests for scheduling. Inherently, the server needs a global scheduling objective to optimize. We mainly study the scheduling objective of minimizing `knorms of flow time of all requests, where 1 ≤ k < ∞. These objectives can be used to balance average performance and fairness. A popular performance measure for online scheduling algorithms is competitive
Deconstructing Intractability  A Multivariate Complexity Analysis of Interval Constrained Coloring
 JOURNAL OF DISCRETE ALGORITHMS, CPM 2009 SPECIAL ISSUE
, 2009
"... The NPhard Interval Constrained Coloring (ICC) problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments. Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to ..."
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Cited by 3 (1 self)
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The NPhard Interval Constrained Coloring (ICC) problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments. Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to be used for its elements), one asks whether there is a “consistent” coloring for all integer points from {1,...,n} that complies with the constraints specified by the color multisets. We thoroughly analyze a known NPhardness proof for ICC. In this way, we identify numerous parameters that naturally occur in ICC and strongly influence its practical solvability. Accordingly, we present several positive (fixedparameter) tractability results exploiting various parameterizations. We substantiate the usefulness of this “multivariate algorithmics approach” by presenting experimental results with realworld data.