Concurrent Geometric Multicasting

We present MCFR, a multicasting concurrent face routing algorithm that uses geometric routing to deliver a message from source to multiple targets. We describe the algorithm's operation, prove it correct, estimate its performance bounds and evaluate its performance using simulation. Our estimate shows that MCFR is the first geometric multicast routing algorithm whose message delivery latency is independent of network size and only proportional to the distance between the source and the targets. Our simulation indicates that MCFR has significantly better reliability than existing algorithms

Approximating max-min linear programs with local algorithms

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise $\min_k \sum_v c_{kv} x_v$ subject to $\sum_v a_{iv} x_v \le 1$ for each $i$ and $x_v \ge 0$ for each $v$. Here $c_{kv} \ge 0$, $a_{iv} \ge 0$, and the support sets $V_i = \{v : a_{iv} > 0 \}$, $V_k = \{v : c_{kv}>0 \}$, $I_v = \{i : a_{iv} > 0 \}$ and $K_v = \{k : c_{kv} > 0 \}$ have bounded size. In the distributed setting, each agent $v$ is responsible for choosing the value of $x_v$, and the communication network is a hypergraph $\mathcal{H}$ where the sets $V_k$ and $V_i$ constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if $|V_i|$ and $|V_k|$ are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in $\mathcal{H}$.Comment: 16 pages, 2 figure

Sharing Memory between Byzantine Processes using Policy-enforced Tuple Spaces

Abstract—Despite the large amount of Byzantine fault-tolerant algorithms for message-passing systems designed through the years, only recent algorithms for the coordination of processes subject to Byzantine failures using shared memory have appeared. This paper presents a new computing model in which shared memory objects are protected by fine-grained access policies, and a new shared memory object, the Policy-Enforced Augmented Tuple Space (PEATS). We show the benefits of this model by providing simple and efficient consensus algorithms. These algorithms are much simpler and require less shared memory operations, using also less memory bits than previous algorithms based on access control lists (ACLs) and sticky bits. We also prove that PEATS objects are universal, i.e., that they can be used to implement any other shared memory object, and present lock-free and wait-free universal constructions. Index Terms—Byzantine fault-tolerance, shared memory algorithms, tuple spaces, consensus, universal constructions. Ç

On Strong Diameter Padded Decompositions

Given a weighted graph G=(V,E,w), a partition of V is Delta-bounded if the diameter of each cluster is bounded by Delta. A distribution over Delta-bounded partitions is a beta-padded decomposition if every ball of radius gamma Delta is contained in a single cluster with probability at least e^{-beta * gamma}. The weak diameter of a cluster C is measured w.r.t. distances in G, while the strong diameter is measured w.r.t. distances in the induced graph G[C]. The decomposition is weak/strong according to the diameter guarantee. Formerly, it was proven that K_r free graphs admit weak decompositions with padding parameter O(r), while for strong decompositions only O(r^2) padding parameter was known. Furthermore, for the case of a graph G, for which the induced shortest path metric d_G has doubling dimension ddim, a weak O(ddim)-padded decomposition was constructed, which is also known to be tight. For the case of strong diameter, nothing was known. We construct strong O(r)-padded decompositions for K_r free graphs, matching the state of the art for weak decompositions. Similarly, for graphs with doubling dimension ddim we construct a strong O(ddim)-padded decomposition, which is also tight. We use this decomposition to construct (O(ddim),O~(ddim))-sparse cover scheme for such graphs. Our new decompositions and cover have implications to approximating unique games, the construction of light and sparse spanners, and for path reporting distance oracles

An Optimised Shortest Path Algorithm for Network Rotuting & SDN: Improvement on Bellman-Ford Algorithm

Network routing algorithms form the backbone of data transmission in modern network architectures, with implications for efficiency, speed, and reliability. This research aims to critically investigate and compare three prominent routing algorithms: Bellman-Ford, Shortest Path Faster Algorithm (SPFA), and our novel improved variant of Bellman-Ford, the Space-efficient Cost-Balancing Bellman-Ford (SCBF). We evaluate the performance of these algorithms in terms of time and space complexity, memory utilization, and routing efficacy, within a simulated network environment. Our results indicate that while Bellman-Ford provides consistent performance, both SPFA and SCBF present improvements in specific scenarios with the SCBF showing notable enhancements in space efficiency. The innovative SCBF algorithm provides competitive performance and greater space efficiency, potentially making it a valuable contribution to the development of network routing protocols. Further research is encouraged to optimize and evaluate these algorithms in real-world network conditions. This study underscores the continuous need for algorithmic innovation in response to evolving network demands

Seluge++: A Secure Over-the-Air Programming Scheme in Wireless Sensor Networks

Over-the-air dissemination of code updates in wireless sensor networks have been researchers’ point of interest in the last few years, and, more importantly, security challenges toward the remote propagation of code updating have occupied the majority of efforts in this context. Many security models have been proposed to establish a balance between the energy consumption and security strength, having their concentration on the constrained nature of wireless sensor network (WSN) nodes. For authentication purposes, most of them have used a Merkle hash tree to avoid using multiple public cryptography operations. These models mostly have assumed an environment in which security has to be at a standard level. Therefore, they have not investigated the tree structure for mission-critical situations in which security has to be at the maximum possible level (e.g., military applications, healthcare). Considering this, we investigate existing security models used in over-the-air dissemination of code updates for possible vulnerabilities, and then, we provide a set of countermeasures, correspondingly named Security Model Requirements. Based on the investigation, we concentrate on Seluge, one of the existing over-the-air programming schemes, and we propose an improved version of it, named Seluge++, which complies with the Security Model Requirements and replaces the use of the inefficient Merkle tree with a novel method. Analytical and simulation results show the improvements in Seluge++ compared to Seluge