Related papers: Better Bounds for Incremental Frequency Allocation…
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational…
The advent of network coding presents promising opportunities in many areas of communication and networking. It has been recently shown that network coding technique can significantly increase the overall throughput of wireless networks by…
In this paper, we explore the design and analysis of regular bipartite graphs motivated by their application in low-density parity-check (LDPC) codes specifically with constrained girth and in the high-rate regime. We focus on the relation…
Suppose there is a spreading process such as an infectious disease propagating on a graph. How would we reduce the number of affected nodes in the spreading process? This question appears in recent studies about implementing mobility…
In this work, we formulate and study a data dissemination problem, which can be viewed as a generalization of the index coding problem and of the data exchange problem to networks with an arbitrary topology. We define $r$-solvable networks,…
The independent set reconfiguration problem asks whether one can transform one given independent set of a graph into another, by changing vertices one by one in such a way the intermediate sets remain independent. Extremal problems on…
In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average…
A challenging problem in multi-band multi-cell self-organized wireless systems, such as multi-channel Wi-Fi networks, femto/pico cells in 3G/4G cellular networks, and more recent wireless networks over TV white spaces, is of distributed…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are interested in the parameter Ie(G), which, for a given graph…
In this paper we consider the multiparty equality problem in graphs, where every vertex of a graph $G$ is given an input, and the goal of the vertices is to decide whether all inputs are equal. We study this problem in the local broadcast…
In this study we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with…
A graph is \textit{locally irregular} if the neighbors of every vertex $v$ have degrees distinct from the degree of $v$. \textit{locally irregular edge-coloring} of a graph $G$ is an (improper) edge-coloring such that the graph induced on…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
We consider the problem of downlink power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To mitigate the interference among concurrent…
In this paper, we present a new factor of IID process based on the local algorithm introduced by D\'iaz, Serna, and Wormald (2007). This new approach allows us to improve the previously known upper bounds on the minimum and maximum…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e.…
Given an undirected graph with edge costs and node weights, the minimum bisection problem asks for a partition of the nodes into two parts of equal weight such that the sum of edge costs between the parts is minimized. We give a polynomial…