On Directed Densest Subgraph Discovery

Given a directed graph G , the directed densest subgraph (DDS) problem refers to the finding of a subgraph from G , whose density is the highest among all the subgraphs of G . The DDS problem is fundamental to a wide range of applications, such as fraud detection, community mining, and graph compression. However, existing DDS solutions suffer from efficiency and scalability problems: on a 3,000-edge graph, it takes three days for one of the best exact algorithms to complete. In this article, we develop an efficient and scalable DDS solution. We introduce the notion of [ x , y ]-core, which is a dense subgraph for G , and show that the densest subgraph can be accurately located through the [ x , y ]-core with theoretical guarantees. Based on the [ x , y ]-core, we develop exact and approximation algorithms. We further study the problems of maintaining the DDS over dynamic directed graphs and finding the weighted DDS on weighted directed graphs, and we develop efficient non-trivial algorithms to solve these two problems by extending our DDS algorithms. We have performed an extensive evaluation of our approaches on 15 real large datasets. The results show that our proposed solutions are up to six orders of magnitude faster than the state-of-the-art.

Improved Lipophilicity and Aqueous Solubility Prediction with Composite Graph Neural Networks

The accurate prediction of molecular properties, such as lipophilicity and aqueous solubility, are of great importance and pose challenges in several stages of the drug discovery pipeline. Machine learning methods, such as graph-based neural networks (GNNs), have shown exceptionally good performance in predicting these properties. In this work, we introduce a novel GNN architecture, called directed edge graph isomorphism network (D-GIN). It is composed of two distinct sub-architectures (D-MPNN, GIN) and achieves an improvement in accuracy over its sub-architectures employing various learning, and featurization strategies. We argue that combining models with different key aspects help make graph neural networks deeper and simultaneously increase their predictive power. Furthermore, we address current limitations in assessment of deep-learning models, namely, comparison of single training run performance metrics, and offer a more robust solution.

An analogue of a theorem of Steinitz for ball polyhedra in $$\mathbb {R}^3$$

Steinitz’s theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if and only if, G is simple, plane and 3-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in $$\mathbb {R}^3$$ R 3 .

OPTIMASI JALUR EVAKUASI BAGI PEJALAN KAKI MENGGUNAKAN ALGORITMA FUZZY DIJKSTRA DI KECAMATAN TELUK SEGARA, BENGKULU

Provinsi Bengkulu terletak di pesisir barat Pulau Sumatera dan tepat berada di antara pertemuan dua lempeng dunia yang sangat aktif yaitu Lempeng Benua Eurasia dan Lempeng Samudra Indo-Australia. Hal ini menyebabkan Provinsi Bengkulu tergolong sebagai provinsi yang sangat rawan terhadap bencana gempa bumi dan tsunami. Penelitian ini mengkaji persoalan optimasi pencarian rute evakuasi tsunami. Tujuan penelitian ini adalah menentukan rute evakuasi dari tiap-tiap cluster yang telah dibentuk menuju tempat berkumpul yang telah ditentukan. Tiap-tiap cluster, titik berkumpul dan ruas jalan yang menghubungkannya dibentuk menjadi suatu graph jaringan jalan dimana cluster dan titik berkumpul diwakili oleh vertex dan ruas jalan diwakili oleh edge. Graph jaringan jalan ini diberi bobot dimana dalam penentuan bobotnya menggunakan logika fuzzy dengan mempertimbangkan beberapa parameter yaitu panjang jalan, lebar jalan, dan jumlah penduduk yang berpengaruh pada tingkat keramaian dan tingkat kemacetan. Penentuan rute optimalnya dilakukan dengan menggunakan algoritma Dijkstra. Berdasarkan hasil penelitian, diperoleh rute optimal dari tiap-tiap cluster menuju tempat berkumpul yang telah ditentukan

Efficient Directed Densest Subgraph Discovery

Given a directed graph G, the directed densest subgraph (DDS) problem refers to the finding of a subgraph from G, whose density is the highest among all the subgraphs of G. The DDS problem is fundamental to a wide range of applications, such as fraud detection, community mining, and graph compression. However, existing DDS solutions suffer from efficiency and scalability problems: on a threethousand- edge graph, it takes three days for one of the best exact algorithms to complete. In this paper, we develop an efficient and scalable DDS solution. We introduce the notion of [x, y]-core, which is a dense subgraph for G, and show that the densest subgraph can be accurately located through the [x, y]-core with theoretical guarantees. Based on the [x, y]-core, we develop both exact and approximation algorithms. We have performed an extensive evaluation of our approaches on eight real large datasets. The results show that our proposed solutions are up to six orders of magnitude faster than the state-of-the-art.

Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms

Directed acyclic graphical models are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs. As the space of directed acyclic graphs on p nodes and the associated space of Markov equivalence classes are both much larger than the space of permutations, it is desirable to consider permutation-based greedy searches. Here, we provide the first consistency guarantees, both uniform and high-dimensional, of a greedy permutation-based search. This search corresponds to a simplex-like algorithm operating over the edge-graph of a subpolytope of the permutohedron, called a directed acyclic graph associahedron. Every vertex in this polytope is associated with a directed acyclic graph, and hence with a collection of permutations that are consistent with the directed acyclic graph ordering. A walk is performed on the edges of the polytope maximizing the sparsity of the associated directed acyclic graphs. We show via simulated and real data that this permutation search is competitive with current approaches.

A pursuit-evasion differential game with slow pursuers on the edge graph of simplexes. I

We consider the differential game between several pursuing points and one evading point moving along the graph of edges of a simplex when maximal quantities of velocities are given. The normalization of the game in the sense of J. von Neumann including the description of classes of admissible strategies is exposed. In the present part of the paper the qualitative problem for the full graph of three dimensional simplex is solved using the strategy of parallel pursuit for a slower pursuer and some numerical coefficient of a simplex characterizing its proximity to the regular one. Next part will be devoted to higher dimensional cases.