Amortized $\tilde{O}(|V|)$ -Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

Ferreira, Rui A. C.; Grossi, Roberto; Rizzi, Roméo; Sacomoto, Gustavo; Sagot, Marie‐France

doi:10.1007/978-3-662-44777-2_35

Cited by 17 publications

(9 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm in Birmelé et al [6] is able to list all simple cycles in a graph in O(m + c∈C(G) |c|), where m is the number of edges, C(G) is the set of simple cycles in graph G and |c| is the size of the cycle. As for induced cycles, the algorithm presented in Ferreira et al [25] has a listing time of Õ(m + nC), with n and C being the number of nodes and induced cycles, respectively. In certain types of graphs, a better complexity can be obtained.…”

Section: A4 Computational Analysismentioning

confidence: 99%

Weisfeiler and Lehman Go Cellular: CW Networks

Bodnar¹,

Frasca²,

Otter³

et al. 2021

Preprint

View full text Add to dashboard Cite

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models are severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and, in certain cases, not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higherorder signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.

show abstract

Section: A4 Computational Analysismentioning

confidence: 99%

Weisfeiler and Lehman Go Cellular: CW Networks

Bodnar¹,

Frasca²,

Otter³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Designing efficient enumeration algorithms, branching (also known as binary partition, flashlight search, and backtracking) is a widely used technique [2,12,27,29,33]. In this technique, given an instance I, we recursively create subinstances I 1 , .…”

Section: A Hardness Of the Minimal Steiner Tree Extension Problemmentioning

confidence: 99%

Linear-Delay Enumeration for Minimal Steiner Problems

Kobayashi¹,

Kurita²,

Wasa³

2020

Preprint

View full text Add to dashboard Cite

Let G = (V, E) be a undirected graph and let W ⊆ V be a set of terminals. A Steiner subgraph of (G, W ) is a subgraph of G that contains all vertices of W and there is a path between every pair of vertices of W in the subgraph. We say that a Steiner subgraph is minimal if it has no proper Steiner subgraph. It is easy to observe that every minimal Steiner subgraph forms a tree, which is called a minimal Steiner tree. We propose a linear delay and polynomial space algorithm for enumerating all minimal Steiner trees of (G, W ), which improves a previously known polynomial delay enumeration algorithm in [Kimelfeld and Sagiv, Inf. Syst., 2008]. Our enumeration algorithm can be extended to other Steiner problems: minimal Steiner forests, minimal terminal Steiner trees, minimal directed Steiner trees. As another variant of the minimal Steiner subgraph problem, we study the problem of enumerating minimal induced Steiner subgraphs. We propose a polynomial delay and exponential space enumeration algorithm of minimal induced Steiner subgraphs for claw-free graphs, whereas the problem on general graphs is shown to be at least as hard as the problem of enumerating minimal transversals in hypergraphs. Contrary to these tractable results, we show that the problem of enumerating minimal group Steiner trees is at least as hard as the minimal transversal enumeration problem on hypergraphs.

show abstract

“…The new algorithm, inspired by the binary partition method [3,14], recursively partitions the solution space at every call until the considered subspace is a singleton (contains only one solution) and in that case outputs the corresponding solution. In order to have an efficient algorithm is important to explore only non-empty partitions.…”

Section: Preliminariesmentioning

confidence: 99%

Efficiently listing bounded length st-paths

Rizzi¹,

Sacomoto²,

Sagot³

2014

Preprint

Self Cite

View full text Add to dashboard Cite

The problem of listing the K shortest simple (loopless) stpaths in a graph has been studied since the early 1960s. For a nonnegatively weighted graph with n vertices and m edges, the most efficient solution is an O(K(mn+n 2 log n)) algorithm for directed graphs by Yen and Lawler [Management Science, 1971 and1972], and an O(K(m + n log n)) algorithm for the undirected version by Katoh et al. [Networks, 1982], both using O(Kn + m) space. In this work, we consider a different parameterization for this problem: instead of bounding the number of st-paths output, we bound their length. For the bounded length parameterization, we propose new non-trivial algorithms matching the time complexity of the classic algorithms but using only O(m + n) space. Moreover, we provide a unified framework such that the solutions to both parameterizations -the classic K-shortest and the new length-bounded paths -can be seen as two different traversals of a same tree, a Dijkstralike and a DFS-like traversal, respectively.⋆ GS and MFS were partially supported by the ERC programme FP7/2007-2013 / ERC grant agreement no.[247073]10, and the French project ANR-12-BS02-0008 (Colib'read).

show abstract

Amortized $\tilde{O}(|V|)$ -Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

Cited by 17 publications

References 14 publications

Weisfeiler and Lehman Go Cellular: CW Networks

Weisfeiler and Lehman Go Cellular: CW Networks

Linear-Delay Enumeration for Minimal Steiner Problems

Efficiently listing bounded length st-paths

Contact Info

Product

Resources

About