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Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes s, t in a greedy embedding there is always a neighbor u of s that is closer to t…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…
Hierarchical embedding constraints define a set of allowed cyclic orders for the edges incident to the vertices of a graph. These constraints are expressed in terms of FPQ-trees. FPQ-trees are a variant of PQ-trees that includes F-nodes in…
We study the problem of low-stretch spanning trees in graphs of bounded width: bandwidth, cutwidth, and treewidth. We show that any simple connected graph $G$ with a linear arrangement of bandwidth $b$ can be embedded into a distribution…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Network embedding, a graph representation learning method illustrating network topology by mapping nodes into lower-dimension vectors, is challenging to accommodate the ever-changing dynamic graphs in practice. Existing research is mainly…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We propose the following conjecture: For every fixed $\alpha\in [0,\frac 13)$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. Our main…
A greedy embedding of a graph $G = (V,E)$ into a metric space $(X,d)$ is a function $x : V(G) \to X$ such that in the embedding for every pair of non-adjacent vertices $x(s), x(t)$ there exists another vertex $x(u)$ adjacent to $x(s)$ which…
Distributed optimization algorithms are frequently faced with solving sub-problems on disjoint connected parts of a network. Unfortunately, the diameter of these parts can be significantly larger than the diameter of the underlying network,…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…