A Review of Interference Reduction in Wireless Networks Using Graph Coloring Methods

The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being focused upon as a problem in today's world. In this paper we analyze the interference reduction problem from a graph theoretical viewpoint. A graph coloring methods are exploited to model the interference reduction problem. However, additional constraints to graph coloring scenarios that account for various networking conditions result in additional complexity to standard graph coloring. This paper reviews a variety of algorithmic solutions for specific network topologies.Comment: 10 pages, 5 figure

Wireless Scheduling with Power Control

We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints. We give an algorithm that attains an approximation ratio of $O(\log n \cdot \log\log \Delta)$, where $n$ is the number of links and $\Delta$ is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on $\Delta$ is unavoidable, showing that any reasonably-behaving oblivious power assignment results in a $\Omega(\log\log \Delta)$-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.Comment: Revised full versio

A note on uniform power connectivity in the SINR model

In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or less colors, corresponding to the number of frequencies or time slots, are necessary. We consider the SINR model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise . The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent $\alpha$. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if $\alpha>1$ as well as in two-dimensional grids if $\alpha>2$. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of $\mathcal{O}(\log n)$ and $\Omega(\log n/\log\log n)$ for $\alpha=2$ and $\Theta(n^{2/\alpha-1})$ for $\alpha<2$ respectively. If nodes are distributed uniformly at random on the interval $[0,1]$, a \emph{regular} coloring of $\mathcal{O}(\log n)$ colors guarantees connectivity, while $\Omega(\log \log n)$ colors are required for any coloring.Comment: 13 page

Visualized Algorithm Engineering on Two Graph Partitioning Problems

Concepts of graph theory are frequently used by computer scientists as abstractions when modeling a problem. Partitioning a graph (or a network) into smaller parts is one of the fundamental algorithmic operations that plays a key role in classifying and clustering. Since the early 1970s, graph partitioning rapidly expanded for applications in wide areas. It applies in both engineering applications, as well as research. Current technology generates massive data (“Big Data”) from business interactions and social exchanges, so high-performance algorithms of partitioning graphs are a critical need. This dissertation presents engineering models for two graph partitioning problems arising from completely different applications, computer networks and arithmetic. The design, analysis, implementation, optimization, and experimental evaluation of these models employ visualization in all aspects. Visualization indicates the performance of the implementation of each Algorithm Engineering work, and also helps to analyze and explore new algorithms to solve the problems. We term this research method as “Visualized Algorithm Engineering (VAE)” to emphasize the contribution of the visualizations in these works. The techniques discussed here apply to a broad area of problems: computer networks, social networks, arithmetic, computer graphics and software engineering. Common terminologies accepted across these disciplines have been used in this dissertation to guarantee practitioners from all fields can understand the concepts we introduce

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum