A polynomial-time algorithm for pliable index coding

Song, Linqi; Fragouli, Christina

doi:10.1109/isit.2016.7541273

Cited by 9 publications

(23 citation statements)

References 20 publications

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“…We call such a problem c-constrained pliable index coding and denote it by (m, n, {R i } i∈[n] , c). In this work, we focus on scalar linear coding as we describe next; we note that vector linear coding was shown to not offer order-of-magnitude benefits for pliable index coding [16]: both scalar and vector linear pliable index coding achieve the lower bound Ω(log(n)) and the upper bound O(log 2 (n)) for the optimal number of broadcast transmissions.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…Clearly, the larger the value of c, the more benefits we expect constrained pliable index coding to have over index coding (for c = n we have exponential benefits [15], [16]). We here provide an example to show that it is possible to have benefits of O(n) even when c = 1, i.e., each message can satisfy at most one client, as is the case in index coding.…”

Section: B Benefits Over Index Codingmentioning

confidence: 99%

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A Pliable Index Coding Approach to Data Shuffling

Song

Fragouli

Zhao

2020

IEEE Trans. Inform. Theory

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A promising research area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shuffling, as it can better leverage the many possible shuffling choices to reduce the number of transmissions. We theoretically analyze pliable index coding under data shuffling constraints, and design a hierarchical data-shuffling scheme that uses pliable coding as a component. We find benefits up to O(ns/m) over index coding, where ns/m is the average number of workers caching a message, and m, n, and s are the numbers of messages, workers, and cache size, respectively. I. INTRODUCTIONA promising research area that has recently emerged, is on how to use coding techniques to improve the communication efficiency in distributed computing systems [2], [3], [4]. In particular, index coding has been proposed to increase the efficiency of data shuffling, that can form a major communication bottleneck for big data applications [2], [4], [5]. In index coding, a server has m messages, and is connected through a broadcast channel to n nodes; each node has a specific request, as well as some side information. The goal is to minimize the number of broadcast transmissions so that, each of the n nodes receives its request. In this paper, we posit that using a form of pliable index coding, a variation of the traditional index coding, can offer a more efficient framework and higher benefits for data shuffling.Data shuffling is used in computational tasks, such as large-scale distributed machine learning over massive data, where local data needs to be shuffled over iterations to train a more robust L. Song and C. Fragouli are with the

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Section: A Problem Formulationmentioning

confidence: 99%

Section: B Benefits Over Index Codingmentioning

confidence: 99%

A Pliable Index Coding Approach to Data Shuffling

Song

Fragouli

Zhao

2020

IEEE Trans. Inform. Theory

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“…We will use the following decoding criterion directly from [12] that determines whether client i is able to decode some new message j ∈ R i , given a certain transmission scheme.…”

Section: Draftmentioning

confidence: 99%

“…This problem is NP hard, but there exist polynomial time algorithms that require in the worst case O(log 2 n) transmissions [12], [13].…”

Section: Past Formulationsmentioning

confidence: 99%

Making recommendations bandwidth aware

Song¹,

Fragouli²

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommender systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenarios where each client has preferences associated with messages.The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenarios we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms.

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“…Song and Fragouli [11] also restricted their analysis to linear codes to show that if receivers having every possible strict This work is supported by the ARC Future Fellowship FT140100219 and by NSF grants CNS-1526547 and CCF-1815322. subset of the message set are present, then the sender needs to send all m messages.…”

Section: Introductionmentioning

confidence: 99%

Optimal-Rate Characterisation for Pliable Index Coding using Absent Receivers

Ong¹,

Vellambi

Kliewer

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We characterise the optimal broadcast rate for a few classes of pliable-index-coding problems. This is achieved by devising new lower bounds that utilise the set of absent receivers to construct decoding chains with skipped messages. This work complements existing works by considering problems that are not complete-S, i.e., problems considered in this work do not require that all receivers with a certain side-information cardinality to be either present or absent from the problem. We show that for a certain class, the set of receivers is critical in the sense that adding any receiver strictly increases the broadcast rate. A. Problem FormulationWe use the following notation: Z + denotes the set of natural numbers, [a : b] := {a, a + 1, . . . , b} for a, b ∈ Z + such that a < b, and X S = (X i : i ∈ S) for some ordered set S.Consider a sender having m ∈ Z + messages, denoted by X [1:m] = (X 1 , . . . , X m ). Each message X i ∈ F q is independently and uniformly distributed over a finite field of size q. There are n receivers having distinct subsets of messages, which we refer to as side information. Each receiver is labelled by its arXiv:1909.11847v1 [cs.IT] 26 Sep 2019Proof: From Lemmas 3 and 4, we know that β q (P m,U ) ≥ min D (m − |S|), for any (C, S) ∈ C for each decoding choice D. By optimising (C, S) ∈ C for each D, we get Lemma 5.Remark 3: Although the lower bound (4) involves minimising over all (C, S) ∈ C, it is clear that any choice of (C, S) for each D will also give us a lower bound. Having said that, maximising over all D is compulsory. E. A lower bound based on nested chains of absent receiversDenote the set of absent receivers by U abs := 2 [1:m] \ ({[1 : m]} ∪ U).Lemma 6: If an instance of Algorithm 1 skips L ∈ Z + messages, then there exists a nested chain of absent receivers of length L, that is, H 1 H 2 · · · H L , with each H i ∈ U abs .Proof: A decoding chain C is constructed by adding messages one by one. So, any receiver that is hit must contain all previously hit receivers. From Remark 2, we know that if the algorithm skips L messages, it must hit L absent receivers, and these absent receivers must form a nested chain.We will now prove another lower bound that is easier to use compared to Lemma 5 in some scenarios (for example, case 2 in Theorem 3 and Theorem 4).Lemma 7: [Lower bound] Consider a pliable-index-coding problem P m,U and its bipartite-graph representation G. Let L ∈ Z + be the maximum length of any nested chain constructed from receivers absent in P m,U . We have that β q (P m,U ) ≥ m − L.Proof: L must be the largest number of skipped messages evaluated over all decoding choices D and skipped-message sets. Otherwise, from Lemma 6, we have a nested chain of absent receivers of length L + 1, which is a contradiction. Thus, m − L = m − max D max (C,S)∈C |S| ≤ m − max D min (C,S)∈C |S| (4) ≤ β q (P m,U ).

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A polynomial-time algorithm for pliable index coding

Cited by 9 publications

References 20 publications

A Pliable Index Coding Approach to Data Shuffling

A Pliable Index Coding Approach to Data Shuffling

Making recommendations bandwidth aware

Optimal-Rate Characterisation for Pliable Index Coding using Absent Receivers

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