Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A New Interference-Alignment Scheme for Wireless MapReduce

Yue Bi, Michèle Wigger, Yue Wu

TL;DR

This work addresses the NDT–computation-load tradeoff in a full-duplex wireless MapReduce system by deriving new upper and lower bounds and proposing an IA-based shuffle scheme. The method leverages $r$-fold cooperation and carefully designed IA precoders to align interference while exploiting MapReduce side information, achieving a tighter upper bound on the NDT than prior schemes. The paper also provides an information-theoretic lower bound on the minimum NDT, establishing regime-dependent optimality: for $r \ge \lceil K/2 \rceil$ linear beamforming, zero-forcing, and interference cancellation are optimal; for $r < \lceil (K-1)/2 \rceil$ these methods become suboptimal. Overall, the results narrow the NDT tradeoff and guide interference-management strategies in wireless MapReduce deployments.

Abstract

We consider a full-duplex wireless Distributed Computing (DC) system under the MapReduce framework. New upper and lower bounds on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load are presented. The upper bound strictly improves over the previous reported upper bounds and is based on a novel interference alignment (IA) scheme tailored to the interference cancellation capabilities of MapReduce nodes. The lower bound is proved through information-theoretic converse arguments.

A New Interference-Alignment Scheme for Wireless MapReduce

TL;DR

This work addresses the NDT–computation-load tradeoff in a full-duplex wireless MapReduce system by deriving new upper and lower bounds and proposing an IA-based shuffle scheme. The method leverages -fold cooperation and carefully designed IA precoders to align interference while exploiting MapReduce side information, achieving a tighter upper bound on the NDT than prior schemes. The paper also provides an information-theoretic lower bound on the minimum NDT, establishing regime-dependent optimality: for linear beamforming, zero-forcing, and interference cancellation are optimal; for these methods become suboptimal. Overall, the results narrow the NDT tradeoff and guide interference-management strategies in wireless MapReduce deployments.

Abstract

We consider a full-duplex wireless Distributed Computing (DC) system under the MapReduce framework. New upper and lower bounds on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load are presented. The upper bound strictly improves over the previous reported upper bounds and is based on a novel interference alignment (IA) scheme tailored to the interference cancellation capabilities of MapReduce nodes. The lower bound is proved through information-theoretic converse arguments.
Paper Structure (14 sections, 7 theorems, 40 equations, 2 figures, 2 tables)

This paper contains 14 sections, 7 theorems, 40 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Wireless MapReduce Framework
  3. Sufficiency of Symmetric File Assignments
  4. Relation to the Sum-DoF with $\mathsf{r}$-fold Cooperation
  5. New IA Scheme
  6. Example 2: $\mathsf{K}=4, \mathsf{r}=2$
  7. The General Scheme
  8. New Bounds on the NDT
  9. Conclusion
  10. Proof of Lemma \ref{['lem:E']}
  11. Analysis of IA Scheme
  12. Proof of the NDT Lower Bound in Theorem \ref{['thm:ndt_bounds']}
  13. Proof of Monotonicity and Convexity of values $C_{i}^{(t)}$
  14. Proof of Structure of Minimizer

Key Result

Lemma 1

For any $\mathsf{r} \in [\mathsf{K}]$:

Figures (2)

  • Figure 1: Bounds on $\Delta^*(\sf r)$ for $\mathsf{K}=11$.
  • Figure 2: Bounds on $\Delta^*(\sf r)$ for $\sf K = 20$.

Theorems & Definitions (11)

  • Lemma 1
  • Remark 1
  • Theorem 1
  • Remark 2
  • Corollary 1
  • Remark 3
  • Corollary 2
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • ...and 1 more