Related papers: On lossy Compression of Directed Graphs
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually…
Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data.…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
This paper considers the joint compression of a pair of correlated sources, where the encoder is allowed to access only one of the sources. The objective is to recover both sources under separate distortion constraints for each source while…
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…
This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…
We consider monotonicity problems for graph searching games. Variants of these games - defined by the type of moves allowed for the players - have been found to be closely connected to graph decompositions and associated width measures such…
Bidirected graphs (earlier studied by Edmonds, Johnson and, in equivalent terms of skew-symmetric graphs, by Tutte, Goldberg, Karzanov, and others) proved to be a useful unifying language for describing both flow and matching problems. In…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuous-alphabet memoryless sources. We show that, for bounded distortion…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
The scene graph is a new data structure describing objects and their pairwise relationship within image scenes. As the size of scene graph in vision applications grows, how to losslessly and efficiently store such data on disks or transmit…
We consider the disordered monomer-dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaussian central limit theorem for the free energy of the…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
Dataset condensation aims to condense a large dataset with a lot of training samples into a small set. Previous methods usually condense the dataset into the pixels format. However, it suffers from slow optimization speed and large number…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…