Search for: All records

This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph on n nodes, and the m edges arrive one by one. The data structure must maintain a topological ordering of the vertices at all times and detect if the newly inserted edge creates a cycle. The theoretically best worst-case algorithms for these problems have high update cost (polynomial in n and m). In practice, greedy heuristics (that recompute the solution from scratch each time) perform well but can have high update cost in the worst case. In this paper, we bridge this gap by leveraging predictions to design a learned new data structure for the problems. Our data structure guarantees consistency, robustness, and smoothness with respect to predictions--that is, it has the best possible running time under perfect predictions, never performs worse than the best-known worst-case methods, and its running time degrades smoothly with the prediction error. Moreover, we demonstrate empirically that predictions, learned from a very small training dataset, are sufficient to provide significant speed-ups on real datasets. 

A growing line of work shows how learned predictions can be used to break through worst-cast barriers to improve the running time of an algorithm. However, incorporating predictions into data structures with strong theoretical guarantees remains underdeveloped. This paper takes a step in this direction by showing that predictions can be leveraged in the fundamental online list labeling problem. In the problem, n items arrive over time and must be stored in sorted order in an array of size Θ(n). The array slot of an element is its label and the goal is to maintain sorted order while minimizing the total number of elements moved (i.e., relabeled). We design a new list labeling data structure and bound its performance in two models. In the worst-case learning-augmented model, we give guarantees in terms of the error in the predictions. Our data structure provides strong theoretical guarantees— it is optimal for any prediction error and guarantees the best-known worst-case bound even when the predictions are entirely erroneous. We also consider a stochastic error model and bound the performance in terms of the expectation and variance of the error. Finally, the theoretical results are demonstrated empirically. In particular, we show that our data structure performs well on numerous real datasets, including temporal datasets where predictions are constructed from elements that arrived in the past (as is typically done in a practical use case).