Related papers: Scheduling wireless links in the physical interfer…
First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph…
In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…
A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$…
In wireless communications, transforming network into graphs and processing them using deep learning models, such as Graph Neural Networks (GNNs), is one of the mainstream network optimization approaches. While effective, the generative AI…
Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not…
An injective $k$-edge-coloring of a graph $G$ is a mapping $\phi$: $E(G)\rightarrow\{1,2,...,k\}$, such that $\phi(e)\ne\phi(e')$ if edges $e$ and $e'$ are at distance two, or are in a triangle. The smallest integer $k$ such that $G$ has an…
In most wireless networks, nodes have only limited local information about the state of the network, which includes connectivity and channel state information. With limited local information about the network, each node's knowledge is…
Let $\chi'_\subset(G)$ be the least number of colours necessary to properly colour the edges of a graph $G$ with minimum degree $\delta\geq 2$ so that the set of colours incident with any vertex is not contained in a set of colours incident…
We study the problem of scheduling packet transmissions with the aim of minimizing the energy consumption and data transmission delay of users in a wireless network in which spatial reuse of spectrum is employed. We approach this problem…
We study throughput-optimum localized link scheduling in wireless networks. The majority of results on link scheduling assume binary interference models that simplify interference constraints in actual wireless communication. While the…
An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident with distinct sets of colors. The minimum number of colors needed for an adjacent vertex…
We consider the following basic link capacity (a.k.a., one-shot scheduling) problem in wireless networks: Given a set of communication links, find a maximum subset of links that can successfully transmit simultaneously. Good performance…
We consider the problem of binary power control, or link scheduling, in wireless interference networks, where the power control policy is trained using graph representation learning. We leverage the interference graph of the wireless…
Given a multigraph $G=(V,E)$, the {\em edge-coloring problem} (ECP) is to color the edges of $G$ with the minimum number of colors so that no two adjacent edges have the same color. This problem can be naturally formulated as an integer…
An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \in \mathbb{Z}^{s \times 4}$, and a vector $\mathbf{p} =…
In single channel wireless networks, concurrent transmission at different links may interfere with each other. To improve system throughput, a scheduling algorithm is necessary to choose a subset of links at each time slot for data…
With the advance of complex large-scale networks, it is becoming increasingly important to understand how selfish and spatially distributed individuals will share network resources without centralized coordinations. In this paper, we…
In this manuscript, we consider the problems of channel assignment in wireless networks and data migration in heterogeneous storage systems. We show that a soft edge coloring approach to both problems gives rigorous approximation…
The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast…
In this paper, we consider the problem of scheduling real-time traffic in wireless networks under a conflict-graph interference model and single-hop traffic. The objective is to guarantee that at least a certain fraction of packets of each…