Shortest Path Distance Approximation Using Deep Learning Techniques

Rizi, Fatemeh Salehi; Schlötterer, Jörg

doi:10.1109/asonam.2018.8508763

Cited by 24 publications

(17 citation statements)

References 38 publications

(39 reference statements)

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“…Nevertheless, both algorithms are parallelizable and there exist GPU implementations [52, 53]. Alternatively, approximate methods with acceptable accuracy have been also proposed for scaling up computations to graphs with millions of edges [54, 55]. Among them, a promising approach is the so-called landmark-based methods [54].…”

Section: Discussionmentioning

confidence: 99%

gGN: learning to represent graph nodes as low-rank Gaussian distributions

Edera

Stegmayer

Milone

2022

Preprint

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Unsupervised learning of node representations from knowledge graphs is critical for numerous downstream tasks, ranging from large-scale graph analysis to measuring semantic similarity between nodes. This study presents gGN as a novel representation that defines graph nodes as Gaussian distributions. Unlike existing representations that approximate such distributions using diagonal covariance matrices, our proposal approximates them using low-rank perturbations. We demonstrate that this low-rank approximation is more expressive and better suited to represent complex asymmetric relations between nodes. In addition, we provide a computationally affordable algorithm for learning the low-rank representations in an unsupervised fashion. This learning algorithm uses a novel loss function based on the reverse Kullback-Leibler divergence and two ranking metrics whose joint minimization results in node representations that preserve not only node depths but also local and global asymmetric relationships between nodes. We assessed the representation power of the low-rank approximation with an in-depth systematic empirical study. The results show that our proposal was significantly better than the diagonal approximation for preserving graph structures. Moreover, gGN also outperformed 17 methods on the downstream task of measuring semantic similarity between graph nodes.

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Section: Discussionmentioning

confidence: 99%

gGN: learning to represent graph nodes as low-rank Gaussian distributions

Edera

Stegmayer

Milone

2022

Preprint

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“…In addition to these coordinate systems, general graph embedding techniques have also been employed to handle shortest path queries. Node2vec and Poincare embeddings were used with a feed forward neural network to approximate shortest paths distances on large social networks and reported an MRE between 3% to 7% (Rizi, Schloetterer, and Granitzer 2018). More recently, graph embeddings have also been learned alongside the distance predictors, to produce representations more specific to the shortest path task.…”

Section: Related Workmentioning

confidence: 99%

Deep Distance Sensitivity Oracles

Jeong¹,

Pham²,

Bhakta³

et al. 2022

Preprint

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One of the most fundamental graph problems is finding a shortest path from a source to a target node. While in its basic forms the problem has been studied extensively and efficient algorithms are known, it becomes significantly harder as soon as parts of the graph are susceptible to failure. Although one can recompute a shortest replacement path after every outage, this is rather inefficient both in time and/or storage. One way to overcome this problem is to shift computational burden from the queries into a pre-processing step, where a data structure is computed that allows for fast querying of replacement paths, typically referred to as a Distance Sensitivity Oracle (DSO). Such a DSO can be constructed, by utilizing the fact that the shortest path in a graph with failures consists of a concatenation of shortest paths in the original graph. That is, one can quickly compute a replacement path by determining a suitable pivot and concatenating the shortest paths from source to pivot and from pivot to target. Unfortunately, finding such a pivot is far from trivial. In this paper, we utilize node2vec, graph attention networks, and multi-layer perceptrons to find pivots such that the lengths of the resulting paths are close to that of the shortest replacement paths. More precisely, we evaluate our technique on a collection of real-world networks and observe that on average the computed replacement paths are longer by merely a few percentages compared to the optimal solution. While DSOs have been extensively studied in the theoretical computer science community, to the best of our knowledge this is the first work to construct DSOs using deep learning techniques. In particular, in this work we first prove the existence of a combinatorial structure and then build on top of it a deep learning algorithm that utilizes the observed combinatorial structure. As mentioned above -we utilize the combinatorial structure of replacement paths as a concatenation of shortest paths and use deep learning to find the pivot nodes for stitching shortest paths into replacement paths.

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“…Also, more recently, using ML techniques to approximate shortest path distances has lead to interesting results. For example, Rizi et al [26] create an estimate for the shortest path distance between two nodes in a two step approach. In the first step, they create a vector embedding for each node, which is generated by deep learning techniques.…”

Section: Related Workmentioning

confidence: 99%

“…These distances are used to compute sample pairs which samples are used to train a feed-forward neural network to approximate the distance between two new nodes. Rizi et al [26] show results on large-scale real-world social networks (more than 1 million nodes). Their method differs from our approach in the sense that an algorithm is created to approximate shortest path distances in a specific large-scale real-world graph, opposed to an algorithm which can be used for any graph from a set of random graphs with similar properties.…”

Section: Related Workmentioning

confidence: 99%

“…An advantage of the landmark-based approach is its scalability to huge graphs, but Kleinberg et al [14] show that strong theoretical guarantees on approximation quality are not provided for landmark-based methods. Qi et al [24] use an idea similar to the one by Rizi et al [26]. But instead of using a two step approach, a single model is used to predict vertex distances and also to create an embedding for a vertex.…”

Section: Related Workmentioning

confidence: 99%

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Dijkstras algorithm with predictions to solve the single-source many-targets shortest-path problem

Feijen¹,

Schäfer²

2021

Preprint

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We study the use of machine learning techniques to solve a fundamental shortest path problem, which is also known as the single-source many targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to compute a shortest path from a given source node to any of several designated target nodes. Basically, our idea is to combine a machine learning approach with an adapted version of Dijkstra's algorithm to solve this problem: Based on the trace of Dijkstra's algorithm, we design a neural network that predicts the shortest path distance after only a few iterations. The prediction is then used to prune the search space explored by Dijkstra's algorithm, which allows us to save a significant fraction of operations on the underlying priority queue. Crucially, our approach always computes the exact shortest path distances, even if the prediction is inaccurate, and never uses more queue operations than the standard algorithm. In fact, we are able to prove a lower bound on the number of queue operations saved by our new algorithm, which depends on the accuracy of the prediction. Our bound applies to arbitrary graphs as long as (some of) the edge weights are drawn at random. Our experimental findings on random graphs confirm these bounds and show that the actual savings are oftentimes significantly higher.

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Shortest Path Distance Approximation Using Deep Learning Techniques

Cited by 24 publications

References 38 publications

gGN: learning to represent graph nodes as low-rank Gaussian distributions

gGN: learning to represent graph nodes as low-rank Gaussian distributions

Deep Distance Sensitivity Oracles

Dijkstras algorithm with predictions to solve the single-source many-targets shortest-path problem

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