Emoji prediction has been widely adopted in most mobile keyboards to improve the quality of user experience. Considering the resource constraints of smartphones, it is promising to deploy well-trained prediction models on edge servers, with which smartphones can carry out emoji prediction in an online fashion. However, a key issue in such a scenario lies in how the smartphone should select a subset of models to achieve high-accuracy and real-time emoji prediction with energy efficiency (a.k.a.themodel selectionproblem). Moreover, part of the system dynamics such as the prediction accuracy and the inference latency of each model are usually unknowna prioriin practice, further complicating the problem. In this paper, with an effective integration of history-aware online learning and online control, we propose the first green edge intelligence scheme to solve the model selection problem for mobile keyboard emoji prediction. Our theoretical analysis and simulation results verify the effectiveness of our proposed scheme in achieving a sub-linear round-averaged regret bound and energy efficiency with a high prediction accuracy and a low latency.

SimRank is an important metric to measure the topological similarity between two nodes in a graph. In particular, single-source and top-k SimRank has numerous applications in recommendation systems, network analysis, and web mining, etc. Mathematically, given a vertex, the computation of single-machine and single-source SimRank mainly lies in matrix-matrix operations. However, it is almost impossible to directly compute on large graphs. Thus, existing works yield to two main operations: a series of random walks, and sparse matrix and dense vector multiplication operations. This brings about high computation cost for SimRank on large graphs. In real-world applications, there is always the query time and accuracy trade-off, which hinders the computation of high-precision SimRank on large-scale graphs. To handle this problem, this paper proposesClipSim, the first GPU-friendly parallel framework that accelerates the single-source SimRank on GPU with accuracy guarantee. We design a novel data structure and GPU-friendly parallel algorithms for efficient computation of all the operations of SimRank on GPU. Moreover, our theoretical derivation enables ClipSim to largely reduce the number of random walks required for each node, while maintaining the same theoretical accuracy as the state-of-the-art algorithm, ExactSim. We conduct extensive experiments on real-world and synthetic datasets to demonstrate the accuracy and efficiency of ClipSim. The results show that compared with ExactSim, ClipSim obtains single-source SimRank vectors with the same accuracy and up to 160× faster computation time.

Emoji prediction has been widely adopted in most mobile keyboards to improve the quality of user experience. Considering the energy limitations of smartphones, it is promising to consider deploying pre-trained prediction models on edge servers, with which smartphones can carry out emoji prediction in an online fashion. However, given a limited connection capacity, a key issue under such a scheme lies in how each smartphone should select a subset of models to achieve high-accuracy and real-time emoji prediction with energy efficiency (a.k.a. the model selection problem). Moreover, part of the system dynamics such as the accuracy and the latency of individual models are usually unknown a priori in practice, further complicating the problem. In this paper, with an effective integration of history-aware online learning and online control, we propose the first green edge intelligence scheme to solve the model selection problem for edge-assisted mobile keyboard emoji prediction. Our theoretical analysis and simulation results verify the effectiveness of our proposed scheme in achieving a sublinear regret bound and energy efficiency with high accuracy and low latency.

We are indebted to Spink and Tiba Spink and Tiba [3] for pointing out that the key technical lemma (Lemma 4) is incorrect in our paper [2]. We tried to make a revision for fixing the gap. However, with the help of mathematical software Lingo, we found that our lemma has counterexamples and its conclusion is incorrect. The Bollobás--Scott conjecture Spink and Tiba [3], “Every $r$-uniform hypergraph with $m$ edges has a vertex partition into $k$ sets with at most $m/k^r+o(m)$ edges in each set,” remains open for $r\ge4$ and seems difficult. The following result shows that Lemma 4 in [2] is wrong even in the case $k=2$.

Let $r\ge 3$ and $k\ge 2$ be fixed integers. Bollobás and Scott conjectured that every $r$-uniform hypergraph with $m$ edges has a vertex partition into $k$ sets with at most $m/k^r+o(m)$ edges in each set, and proved the conjecture in the case $r=3$. In this paper, we confirm this conjecture in the case $r=4$ by showing that every 4-uniform hypergraph with $m$ edges has a vertex partition into $k$ sets with at most $m/k^4+O(m^{8/9})$ edges in each set.

Abstract An f‐coloring of a multigraph G is a coloring of the edges of E such that each color appears at each vertex v ∈ V at most f(v) times. The minimum number of colors needed to f‐color G is called the f‐chromatic index of G and is denoted by χ′f(G). Various scheduling problems on networks are reduced to finding an f‐coloring of a multigraph. Any simple graph G has f‐chromatic index equal to Δf(G) or Δf(G)+ 1, where Δf(G) = max v∈V{⌈ ${d(v)\over f(v)}$ ⌉} and d(v) is the degree of vertex v. A connected graph G is called f‐critical if χ′f(G)=Δf(G)+1 and χ′f(G)=Δf(G−e) < χ′f(G) for any edge e ∈ E. Some results about f‐critical graphs are given. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(3), 197–202 2007