Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

Ageev, Alexander A.; Sviridenko, Maxim

doi:10.1023/b:joco.0000038913.96607.c2

Cited by 298 publications

(410 citation statements)

References 20 publications

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“…This forest F is the structure that we start with; we show how to round those x i,j in F . We are motivated by the approaches of [1,13,7]; however, our method is different, especially in step (P2) below. Each iteration is described next.…”

Section: The Algorithm and Analysismentioning

confidence: 99%

Budgeted Allocations in the Full-Information Setting

Srinivasan

Lecture Notes in Computer Science

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Section: The Algorithm and Analysismentioning

confidence: 99%

Budgeted Allocations in the Full-Information Setting

Srinivasan

Lecture Notes in Computer Science

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“…Now, if f (P r ∪( C r−1 ∩OPT)) ≥ (1−ǫ)·f (OPT) then this fact together with (1) imply that the first property in the statement of Theorem 4.2 must hold. Otherwise, f (OPT) − f (P r ∪ ( C r−1 ∩ OPT)) ≥ ǫ · f (OPT); this fact together with (2) implies that the second property must hold.…”

Section: (Consistency) Letmentioning

confidence: 99%

“…The DCGreedy algorithm is a heavily discretized version of the measured continuous greedy approach of [15], and it first constructs an approximate fractional solution to the problem max x∈P (I) F (x) of maximizing the multilinear extension F of f subject to the constraint that x is in the matroid polytope P (I), and then rounds the fractional solution without loss using pipage rounding or swap rounding [1,10].…”

Section: A Parallel Continuous Greedy Algorithmmentioning

confidence: 99%

A New Framework for Distributed Submodular Maximization

Barbosa

Ene

Nguyêݱn

et al. 2016

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)

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A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algorithms for these problems. However, these results suffer from high number of rounds, suboptimal approximation ratios, or both. We develop a framework for bringing existing algorithms in the sequential setting to the distributed setting, achieving near optimal approximation ratios for many settings in only a constant number of MapReduce rounds. Our techniques also give a fast sequential algorithm for non-monotone maximization subject to a matroid constraint.

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“…Acharya et al first proposed the scheduling problem for data broadcast [1], and Prabhakara et al suggested the multi-channel model for data broadcast to improve the data delivery performance [14]. Since then, many works have been done for scheduling data on multiple channels to reduce the expected access time [20,22,2]. Besides, some researches began to study how to allocate dependent data on broadcast channels (see, e.g., [10,19,21,5,6]).…”

Section: Related Workmentioning

confidence: 99%

Heuristic Algorithm for Efficient Data Retrieval Scheduling in the Multichannel Wireless Broadcast Environments

Porselvi¹,

Devi²

2015

IJCATR

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Wireless data broadcast is an efficient way of disseminating data to users in the mobile computing environments. From the server's point of view, how to place the data items on channels is a crucial issue, with the objective of minimizing the average access time and tuning time. Similarly, how to schedule the data retrieval process for a given request at the client side such that all the requested items can be downloaded in a short time is also an important problem. In this paper, we investigate the multi-item data retrieval scheduling in the push-based multichannel broadcast environments. The most important issues in mobile computing are energy efficiency and query response efficiency. However, in data broadcast the objectives of reducing access latency and energy cost can be contradictive to each other. Consequently, we define a new problem named Minimum Cost Data Retrieval Problem (MCDR) and Large Number Data Retrieval (LNDR) Problem. We also develop a heuristic algorithm to download a large number of items efficiently. When there is no replicated item in a broadcast cycle, we show that an optimal retrieval schedule can be obtained in polynomial time.

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Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

Cited by 298 publications

References 20 publications

Budgeted Allocations in the Full-Information Setting

Budgeted Allocations in the Full-Information Setting

A New Framework for Distributed Submodular Maximization

Heuristic Algorithm for Efficient Data Retrieval Scheduling in the Multichannel Wireless Broadcast Environments

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