Related papers: A Graph Minor Perspective to Multicast Network Cod…
We study graphs where each edge adjacent to a vertex of small degree (7 and 9, respectively) belongs to many triangles (4 and 5, respectively) and show that these graphs contain a complete graph (K_6 and K_7, respectively) as a minor. The…
We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear time-invariant systems by appropriately restricting channels and coding schemes of network coding to be linear…
Graph Neural Networks (GNNs) have received a lot of interest in the recent times. From the early spectral architectures that could only operate on undirected graphs per a transductive learning paradigm to the current state of the art…
As evidence for the Odd Hadwiger Conjecture, Simonyi and Zsb\'an (2010) showed that every Kneser graph $G$ with large enough order (compared to $\chi(G)$) contains a totally odd subdivision of $K_{\chi(G)}$. A recent result of Steiner…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is…
Information diffusion, spreading of infectious diseases, and spreading of rumors are fundamental processes occurring in real-life networks. In many practical cases, one can observe when nodes become infected, but the underlying network,…
Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising performance for various applications, the huge sizes of graphs may…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
We propose a mechanism that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in…
We consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can be arbitrary. Secure…
Under the reconfiguration framework, we consider the various ways that a target graph $H$ is a {\em minor} of a host graph $G$, where a subgraph of $G$ can be transformed into $H$ by means of {\em edge contraction} (replacement of both…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…
The knowledge of the topology of a wired network is often of fundamental importance. For instance, in the context of Power Line Communications (PLC) networks it is helpful to implement data routing strategies, while in power distribution…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
A $K_t$-expansion consists of $t$ vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be two-colored so that the edges of the trees are bichromatic but the edges between trees…
A (minimal) transversal of a partition is a set which contains exactly one element from each member of the partition and nothing else. A coloring of a graph is a partition of its vertex set into anticliques, that is, sets of pairwise…
This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…