33 research outputs found
Penentuan Prioritas pada Jaringan Back-bone Palapa Ring Menggunakan Derajat Node dan Cut Vertex
Palapa Ring is a project aiming to connect provinces and cities in Indonesia via a high data speed telecommunication path. The purpose of this research is to identify the priority scale of each node in Palapa Ring Backbone network by considering the degree of each node and the cut vertices of the network. The result shows that the existing infrastructure in Palapa Ring comprised 48 nodes and 117 links. The nodes with the highest degree in the network were PBR, PTK, BJM, JK, SB and UP, with each of the nodes was connected to four links. Cut vertices in the network consisted of 22 nodes. The nodes in the network are classified into 4 categories. Five nodes (PBR, PTK, BJM, SB and UP) fell into the 1st priority group, two nodes (JK,MDN) fell into the 2nd priority group, 16 nodes fell into the 3rd priority group and the rest fell into the non priority group
Changepoint Detection over Graphs with the Spectral Scan Statistic
We consider the change-point detection problem of deciding, based on noisy
measurements, whether an unknown signal over a given graph is constant or is
instead piecewise constant over two connected induced subgraphs of relatively
low cut size. We analyze the corresponding generalized likelihood ratio (GLR)
statistics and relate it to the problem of finding a sparsest cut in a graph.
We develop a tractable relaxation of the GLR statistic based on the
combinatorial Laplacian of the graph, which we call the spectral scan
statistic, and analyze its properties. We show how its performance as a testing
procedure depends directly on the spectrum of the graph, and use this result to
explicitly derive its asymptotic properties on few significant graph
topologies. Finally, we demonstrate both theoretically and by simulations that
the spectral scan statistic can outperform naive testing procedures based on
edge thresholding and testing
Isoperimetric Inequalities in Simplicial Complexes
In graph theory there are intimate connections between the expansion
properties of a graph and the spectrum of its Laplacian. In this paper we
define a notion of combinatorial expansion for simplicial complexes of general
dimension, and prove that similar connections exist between the combinatorial
expansion of a complex, and the spectrum of the high dimensional Laplacian
defined by Eckmann. In particular, we present a Cheeger-type inequality, and a
high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach,
we obtain a connection between spectral properties of complexes and Gromov's
notion of geometric overlap. Using the work of Gunder and Wagner, we give an
estimate for the combinatorial expansion and geometric overlap of random
Linial-Meshulam complexes
Distributed Sparse Cut Approximation
We study the problem of computing a sparse cut in an undirected network graph G=(V,E). We measure the sparsity of a cut (S,VS) by its conductance phi(S), i.e., by the ratio of the number of edges crossing the cut and the sum of the degrees on the smaller of the two sides. We present an efficient distributed algorithm to compute a cut of low conductance. Specifically, given two parameters b and phi, if there exists a cut of balance at least b and conductance at most phi, our algorithm outputs a cut of balance at least b/2 and conductance at most ~O(sqrt{phi}), where ~O(.) hides polylogarithmic factors in the number of nodes n. Our distributed algorithm works in the congest model, i.e., it only requires to send messages of size at most O(log(n)) bits. The time complexity of the algorithm is ~O(D + 1/b*phi), where D is the diameter of G. This is a significant improvement over a result by Das Sarma et al. [ICDCN 2015], where it is shown that a cut of the same quality can be computed in time ~O(n + 1/b*phi). The improved running time is in particular achieved by devising and applying an efficient distributed algorithm for the all-prefix-sums problem in a distributed search tree. This algorithm, which is based on the classic parallel all-prefix-sums algorithm, might be of independent interest
SCE: Scalable Network Embedding from Sparsest Cut
Large-scale network embedding is to learn a latent representation for each
node in an unsupervised manner, which captures inherent properties and
structural information of the underlying graph. In this field, many popular
approaches are influenced by the skip-gram model from natural language
processing. Most of them use a contrastive objective to train an encoder which
forces the embeddings of similar pairs to be close and embeddings of negative
samples to be far. A key of success to such contrastive learning methods is how
to draw positive and negative samples. While negative samples that are
generated by straightforward random sampling are often satisfying, methods for
drawing positive examples remains a hot topic.
In this paper, we propose SCE for unsupervised network embedding only using
negative samples for training. Our method is based on a new contrastive
objective inspired by the well-known sparsest cut problem. To solve the
underlying optimization problem, we introduce a Laplacian smoothing trick,
which uses graph convolutional operators as low-pass filters for smoothing node
representations. The resulting model consists of a GCN-type structure as the
encoder and a simple loss function. Notably, our model does not use positive
samples but only negative samples for training, which not only makes the
implementation and tuning much easier, but also reduces the training time
significantly.
Finally, extensive experimental studies on real world data sets are
conducted. The results clearly demonstrate the advantages of our new model in
both accuracy and scalability compared to strong baselines such as GraphSAGE,
G2G and DGI.Comment: KDD 202
Sparsest Cut on Bounded Treewidth Graphs: Algorithms and Hardness Results
We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in
time , where is the treewidth of the graph. This improves on the
previous -approximation in time \poly(n) 2^{O(k)} due to
Chlamt\'a\v{c} et al.
To complement this algorithm, we show the following hardness results: If the
Non-Uniform Sparsest Cut problem has a -approximation for series-parallel
graphs (where ), then the Max Cut problem has an algorithm with
approximation factor arbitrarily close to . Hence, even for such
restricted graphs (which have treewidth 2), the Sparsest Cut problem is NP-hard
to approximate better than for ; assuming the
Unique Games Conjecture the hardness becomes . For
graphs with large (but constant) treewidth, we show a hardness result of assuming the Unique Games Conjecture.
Our algorithm rounds a linear program based on (a subset of) the
Sherali-Adams lift of the standard Sparsest Cut LP. We show that even for
treewidth-2 graphs, the LP has an integrality gap close to 2 even after
polynomially many rounds of Sherali-Adams. Hence our approach cannot be
improved even on such restricted graphs without using a stronger relaxation
CLIMP: Clustering Motifs via Maximal Cliques with Parallel Computing Design.
A set of conserved binding sites recognized by a transcription factor is called a motif, which can be found by many applications of comparative genomics for identifying over-represented segments. Moreover, when numerous putative motifs are predicted from a collection of genome-wide data, their similarity data can be represented as a large graph, where these motifs are connected to one another. However, an efficient clustering algorithm is desired for clustering the motifs that belong to the same groups and separating the motifs that belong to different groups, or even deleting an amount of spurious ones. In this work, a new motif clustering algorithm, CLIMP, is proposed by using maximal cliques and sped up by parallelizing its program. When a synthetic motif dataset from the database JASPAR, a set of putative motifs from a phylogenetic foot-printing dataset, and a set of putative motifs from a ChIP dataset are used to compare the performances of CLIMP and two other high-performance algorithms, the results demonstrate that CLIMP mostly outperforms the two algorithms on the three datasets for motif clustering, so that it can be a useful complement of the clustering procedures in some genome-wide motif prediction pipelines. CLIMP is available at http://sqzhang.cn/climp.html