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The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
In parallel computing, a valid graph coloring yields a lock-free processing of the colored tasks, data points, etc., without expensive synchronization mechanisms. However, coloring is not free and the overhead can be significant. In…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction…
We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight…
We revisit the classical problem of channel allocation for Wi-Fi access points (AP). Using mechanisms such as the CSMA/CA protocol, Wi-Fi access points which are in conflict within a same channel are still able to communicate to terminals.…
The problem of finding a minimum vertex cover (MVC) in a graph is a well-known NP-hard problem with significant practical applications in optimization and scheduling. Its complexity, combined with the increasing scale of problems,…
Graph colorings is a fundamental topic in graph theory that require an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
The semistrong edge coloring, as a relaxation of the well-known strong edge coloring, can be used to model efficient communication scheduling in wireless networks. An edge coloring of a graph $G$ is called \emph{semistrong} if every color…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
Recently multi-channel multi-radio wireless mesh networks are considered a reliable and cost effective way for internet access in wide area. A major research challenge in this network is selecting least interference channel from available…
A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL) are edge-weighted graphs G and the objective is to find…
Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…
The present work deals with the problem of efficiently assigning Wi-Fi channels in a real-world scenario, the Polytechnic School of the University of Alcal\'a. We first use proximity graphs to model the whole problem as an instance of…