# Function Load Balancing Over Networks

@article{Malak2020FunctionLB, title={Function Load Balancing Over Networks}, author={Derya Malak and Muriel M'edard}, journal={IEEE Journal on Selected Areas in Information Theory}, year={2020}, volume={2}, pages={1041-1056} }

Using networks as a means of computing can reduce the communication flow over networks. We propose to distribute the computation load in stationary networks and formulate a flow-based delay minimization problem that jointly captures the costs of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information. We introduce the notion of entropic surjectivity as a measure of function’s sparsity and to understand the…

## References

SHOWING 1-10 OF 54 REFERENCES

### Network Flows for Function Computation

- Computer ScienceIEEE Journal on Selected Areas in Communications
- 2013

This work designs computing and communicating schemes to obtain the function at the terminal at the maximum rate, and develops a fast combinatorial primal-dual algorithm to obtain near-optimal solutions to these linear programs.

### On Network Functional Compression

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2014

A rate region is characterized by introducing a necessary and sufficient condition for any achievable coloring-based coding scheme called coloring connectivity condition and a modularized coding scheme based on graph colorings to perform arbitrarily closely to rate lower bounds is proposed.

### Comments on Cut-Set Bounds on Network Function Computation

- Computer ScienceIEEE Transactions on Information Theory
- 2018

This paper analyzes the reason of the invalidity and proposes a general cut-set bound by using a new equivalence relation associated with the inputs of the target function, which is not valid for general network function computation problems.

### A Fundamental Tradeoff Between Computation and Communication in Distributed Computing

- Computer ScienceIEEE Transactions on Information Theory
- 2018

A coded scheme, named “coded distributed computing” (CDC), is proposed to demonstrate that increasing the computation load of the Map functions by a factor of r can create novel coding opportunities that reduce the communication load by the same factor.

### Functional Compression Through Graph Coloring

- Computer ScienceIEEE Transactions on Information Theory
- 2010

The problem of functional compression is considered, motivated by applications to sensor networks and privacy preserving databases, and an asymptotic characterization of conditional graph coloring for an OR product of graphs generalizing a result of Korner (1973), is obtained.

### A Random Linear Network Coding Approach to Multicast

- Computer ScienceIEEE Transactions on Information Theory
- 2006

This work presents a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks, and shows that this approach can take advantage of redundant network capacity for improved success probability and robustness.

### On distributed function computation in structure-free random networks

- Computer Science2008 IEEE International Symposium on Information Theory
- 2008

A minimal structure (knowledge of hop-distance from the sink) is imposed on the network and with this structure, a protocol for pipelined computation of MAX is described that achieves a rate of Omega(1/(log2 n)).

### Computing Linear Functions by Linear Coding Over Networks

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2014

This work identifies a class of linear functions that can be computed using linear codes in every network that satisfies a natural cut-based condition and shows that the cut- based condition does not guarantee the existence of a linear coding solution.

### Computing and communicating functions over sensor networks

- Computer ScienceIEEE Journal on Selected Areas in Communications
- 2005

The maximum rate at which functions of sensor measurements can be computed and communicated to the sink node is studied, focusing on symmetric functions, where only the data from a sensor is important, not its identity.

### Compressive sensing over networks

- Computer Science2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2010

This paper makes a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding and proposes a compression scheme for a family of correlated sources with a modularized decoder, providing a trade-off between the compression rate and the decoding complexity.