In a distributed environment where IoT devices collaborate on shared data, ensuring a secure turn-taking process during data updates remains crucial. Unlike in centralized systems, the concept of mutexes is no longer applicable in distributed systems. ...

A binary de Bruijn sequence (dB sequence) of order k is a circular binary string that contains each k-length word exactly once as a substring. Most existing algorithms construct a specific dB sequence, or members of a specific class of dB ...

With the rapid development of network technologies such as the Internet of Things, the scale of networks has gradually increased. The P2P networks have been gradually studied, and fault detection and localization for large-scale networks have become a ...

We study the $\kappa$-Colored Constrained Spanning Tree ($\kappa$-CCST) and the $\kappa$-Colored Out-Constrained Spanning Tree ($\kappa$-COCST) problems on edge-colored directed graphs. These problems target to find a spanning tree such that for each vertex, the number of ...$$$$$$$$

Undirected multiple graphs of any natural multiplicity k > 1 are studied. There are edges of three types: ordinary edges, multiple edges, and multi-edges. Each edge of the last two types is a union of k linked edges, which connect 2 or (k + 1) ...

Detecting strongly connected components (SCCs) in a directed graph is crucial for understanding the structure of graphs. Most real-world graphs have one large SCC that contains the majority of the vertices as well as many small SCCs whose sizes are ...

We tackle an optimization problem arising in the design of sensor networks: given a set of sensors, only one being connected to a backbone, to establish connection routes from each of them to the sink. Under a shortest path routing protocol, the set of ...

In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems of graph Laplacians. In earlier works such estimates were computed by solving a perturbed global optimization problem, which could be ...

The central node of traditional mobile transactions is vulnerable to attack and causes user privacy disclosure. To solve this problem, blockchain and mobile transactions are combined to construct a decentralised mobile trading platform. This paper designs ...

This research investigates the pair formation problem described as forming pairs of people to achieve certain objectives. This problem is a subcategory of the well-known grouping problem that is classified as NP-complete. The necessity of pairing people ...

Population protocols [3] are used as a distributed model that captures the behavior of passively mobile agents. Leader election is one of the most well-studied problems in this model. In this paper, we focus on the self-stabilizing leader election (SSLE)...

In a wireless sensor network, aggregation is either done to avoid the redundant transmissions. In service provisioning, the control packets sent for service advertisement and discovery contribute significantly to the network traffic. In this paper, it is ...

The flip graph of triangulations has as vertices all triangulations of a convex $n$-gon and an edge between any two triangulations that differ in exactly one edge. An $r$-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation ...

The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree T for graph G, such that the maximum degree of T is the smallest among all spanning trees of G. Let d be this MDST degree for a given graph. In this paper, we ...

Free-motion quilting patterns are functional and decorative patterns sewn on pieced quilts using a single-line continuous stitch path for each region of the quilt. Seven families of quilting patterns are commonly used by quilters [3]. We present an ...

In this paper, we propose a general scheme, called Algorithm STIC, to compute spanning-tree-like data structures on arbitrary networks. STIC is self-stabilizing and silent and, despite its generality, is also efficient. It is written in the locally ...

Wireless sensor networks consist of sensor devices with limited computational capabilities and memory operating in bounded energy resources; hence, network optimisation and algorithmic development in minimising the total energy or power while maintaining ...

We prove that any weighted graph $G=(V,E,w)$ with $n$ points and $m$ edges has a spanning tree $T$ such that $\sum_{\{u,v\}\in E}\frac{d_T(u,v)}{w(u,v)}=O(m\log n\log\log n)$. Moreover, such a tree can be found in time $O(m\log n\log\log n)$. Our result is ...

Rigidity, arising in discrete geometry, is the property of a structure that does not flex. Laman provides a combinatorial characterization of rigid graphs in the Euclidean plane, and thus rigid graphs in the Euclidean plane have applications in graph ...

Given a family F and a host graph H, a graph Gï źH is F-saturated relative to H if no subgraph of G lies in F but adding any edge from EH-EG to G creates such a subgraph. In the F-saturation game on H, players Max and Min alternately add edges of H to G,...