Related papers: Permutation Routing on Ramanujan Hypergraphs with …

A geometric graph in the plane is angle-monotone of width $\gamma$ if every pair of vertices is connected by an angle-monotone path of width $\gamma$, a path such that the angles of any two edges in the path differ by at most $\gamma$.…

Let $P$ be an $x$-monotone orthogonal polygon with $n$ vertices. We call $P$ a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two…

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind { ($N$-matrix for short)} introduced by Mohar \cite{0001}. This matrix is indexed by the vertices of the mixed…

Effective routing of entanglements over a quantum network is a fundamental problem in quantum communication. Due to the fragility of quantum states, it is difficult to route entanglements at long distances. Graph states can be utilized for…

Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest…

Franceschetti et al. have recently shown that per-node throughput in an extended, ad hoc wireless network with $\Theta(n)$ randomly distributed nodes and multihop routing can be increased from the $\Omega({1 \over \sqrt{n} \log n})$ scaling…

Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly,…

A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus $g$ 2-surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes…

Graph-based semi-supervised learning is a powerful paradigm in machine learning for modeling and exploiting the underlying graph structure that captures the relationship between labeled and unlabeled data. A large number of classical as…

We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity $\mu$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs…

This is the beginning of an obstruction theory for deciding whether a map f:S^2 --> X^4 is homotopic to a topologically flat embedding, in the presence of fundamental group and in the absence of dual spheres. The first obstruction is Wall's…

Let $G$ be a large-girth $d$-regular graph and $\mu$ be a random process on the vertices of $G$ produced by a randomized local algorithm. We prove the upper bound $(k+1-2k/d)\Bigl(\frac{1}{\sqrt{d-1}}\Bigr)^k$ for the (absolute value of…

Hypergraphs are the natural description of higher-order interactions among objects, widely applied in social network analysis, cross-modal retrieval, etc. Hypergraph Neural Networks (HGNNs) have become the dominant solution for learning on…

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame…

We design an algorithm for computing connectivity in hypergraphs which runs in time $\hat O_r(p + \min\{\lambda^{\frac{r-3}{r-1}} n^2, n^r/\lambda^{r/(r-1)}\})$ (the $\hat O_r(\cdot)$ hides the terms subpolynomial in the main parameter and…

Packet routing in nanonetworks requires novel approaches, which can cope with the extreme limitations posed by the nano-scale. Highly lossy wireless channels, extremely limited hardware capabilities and non-unique node identifiers are among…

We model human mobility as a combinatorial allocation process, treating trips as distinguishable balls assigned to location-bins and generating origin-destination (OD) networks. From this analogy, we construct a unified three-scale…

Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing,…

An \textit{\(m \times n\) grid graph} is the induced subgraph of the square lattice whose vertex set consists of all integer grid points \(\{(i,j) : 0 \leq i < m,\ 0 \leq j < n\}\). Let $H$ and $K$ be Hamiltonian cycles in an $m \times n$…

Dynamic low altitude networks offer significant potential for efficient and reliable data transport via unmanned aerial vehicles (UAVs) relays which usually operate with predetermined trajectories. However, it is challenging to optimize the…