Storage Capacity of Repairable Networks

Mazumdar, Arya

doi:10.1109/tit.2015.2472521

Cited by 40 publications

(56 citation statements)

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“…Then the maximum amount of information that can be stored in the graph is called the storage capacity of that graph [17]. This formulation is mainly motivated by applications in distributed storage, and generalizes the popular definition of locally repairable codes [13].…”

Section: Introductionmentioning

confidence: 99%

“…In [17], it was observed that the storage capacity is upper bounded by the size of the minimum vertex cover VC(G) of the graph G.…”

Section: Introductionmentioning

confidence: 99%

“…Because of this, we think it is natural to view storage capacity as an information theoretic analogue of vertex cover. It was also shown in [17] that the storage capacity is at least equal to the size MM(G) of the maximum matching of the graph G:…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [17] that storage capacity is, in a coding-theoretic sense, dual to index coding and is equivalent to the guessing game problem of [12]. The index coding rate for a graph G is defined to be the optimum value of the following minimization problem:…”

Section: Introductionmentioning

confidence: 99%

“…In particular it can be shown that any network coding problem can be reduced to an index coding problem [11]. It has been shown [17] that,…”

Section: Introductionmentioning

confidence: 99%

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Storage capacity as an information-theoretic analogue of vertex cover

Mazumdar

McGregor

Vorotnikova

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic analogue of the minimum vertex cover of a graph. Indeed, while it was known that storage capacity is upper bounded by minimum vertex cover, we show that by treating it as such we can get a 3/2 approximation for planar graphs, and a 4/3 approximation for triangle-free planar graphs. Since the storage capacity is intimately related to the index coding rate, we get a 2 approximation of index coding rate for planar graphs 1 and 3/2 approximation for triangle-free planar graphs. Previously only a trivial 4 approximation of the index coding rate was known for planar graphs. We then develop a general method of "gadget covering" to upper bound the storage capacity in terms of the average of a set of vertex covers. This method is intuitive and leads to the exact characterization of storage capacity for various families of graphs. As an illustrative example, we use this approach to derive the exact storage capacity of cycles-with-chords, a family of graphs related to outerplanar graphs. Finally, we generalize the storage capacity notion to include recovery from partial failures in distributed storage. We show tight upper and lower bounds on this partial recovery capacity that scales nicely with the fraction of failure in a vertex.

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Section: Introductionmentioning

confidence: 99%

“…In [17], it was observed that the storage capacity is upper bounded by the size of the minimum vertex cover VC(G) of the graph G.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In particular it can be shown that any network coding problem can be reduced to an index coding problem [11]. It has been shown [17] that,…”

Section: Introductionmentioning