Extending Karger's randomized min-cut Algorithm for a Synchronous Distributed setting

A min-cut that seperates vertices s and t in a network is an edge set of minimum weight whose removal will disconnect s and t. This problem is the dual of the well known s-t max-flow problem. Several algorithms for the min-cut problem are based on max-flow computation although the fastest known min-cut algorithms are not flow based. The well known Karger's randomized algorithm for min-cut is a non-flow based method for solving the (global) min-cut problem of finding the min s-t cut over all pair of vertices s,t in a weighted undirected graph. This paper presents an adaptation of Karger's algorithm for a synchronous distributed setting where each node is allowed to perform only local computations. The paper essentially addresses the technicalities involved in circumventing the limitations imposed by a distributed setting to the working of Karger's algorithm. While the correctness proof follows directly from Karger's algorithm, the complexity analysis differs significantly. The algorithm achieves the same probability of success as the original algorithm with O(mn^{2}) message complexity and O(n^{2}) time complexity, where n and m denote the number of vertices and edges in the graph.Comment: 6 page

Distributed strategies for generating weight-balanced and doubly stochastic digraphs

Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of cooperative control problems, including formation control, distributed averaging, and optimization. We refer to a digraph as doubly stochasticable (weight-balanceable) if it admits a doubly stochastic (weight-balanced) adjacency matrix. This paper studies the characterization of both classes of digraphs, and introduces distributed algorithms to compute the appropriate set of weights in each case

HushRelay: A Privacy-Preserving, Efficient, and Scalable Routing Algorithm for Off-Chain Payments

Payment channel networks (PCN) are used in cryptocurrencies to enhance the performance and scalability of off-chain transactions. Except for opening and closing of a payment channel, no other transaction requests accepted by a PCN are recorded in the Blockchain. Only the parties which have opened the channel will know the exact amount of fund left at a given instant. In real scenarios, there might not exist a single path which can enable transfer of high value payments. For such cases, splitting up the transaction value across multiple paths is a better approach. While there exists several approaches which route transactions via several paths, such techniques are quite inefficient, as the decision on the number of splits must be taken at the initial phase of the routing algorithm (e.g., SpeedyMurmur [42]). Algorithms which do not consider the residual capacity of each channel in the network are susceptible to failure. Other approaches leak sensitive information, and are quite computationally expensive [28]. To the best of our knowledge, our proposed scheme HushRelay is an efficient privacy preserving routing algorithm, taking into account the funds left in each channel, while splitting the transaction value across several paths. Comparing the performance of our algorithm with existing routing schemes on real instances (e.g., Ripple Network), we observed that HushRelay attains a success ratio of 1, with an execution time of 2.4 sec. However, SpeedyMurmur [42] attains a success ratio of 0.98 and takes 4.74 sec when the number of landmarks is 6. On testing our proposed routing algorithm on the Lightning Network, a success ratio of 0.99 is observed, having an execution time of 0.15 sec, which is 12 times smaller than the time taken by SpeedyMurmur.Comment: 9 pages, 16 figures, 1 table, accepted to the Short Paper track of the 2020 IEEE International Conference on Blockchain and Cryptocurrency (ICBC 2020

Efficient Algorithms for Densest Subgraph Discovery

Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims to find a subgraph D of G with the highest density (e.g., the number of edges over the number of vertices in D). Because DSD is difficult to solve, we propose a new solution paradigm in this paper. Our main observation is that a densest subgraph can be accurately found through a k-core (a kind of dense subgraph of G), with theoretical guarantees. Based on this intuition, we develop efficient exact and approximation solutions for DSD. Moreover, our solutions are able to find the densest subgraphs for a wide range of graph density definitions, including clique-based and general pattern-based density. We have performed extensive experimental evaluation on eleven real datasets. Our results show that our algorithms are up to four orders of magnitude faster than existing approaches

A Distributed Algorithm for the Maximum Flow Problem

This paper presents an asynchronous distributed algorithm for solving the maximum flow problem which is based on the preflow-push approach of Golberg-Tarjan. Each node in graph initially knows the capacities of outgoing and incoming adjacent arcs, the source nodes knows additionally the number of nodes in graph. Nodes execute the same algorithm, and exchange messages with neighbors until the maximum flow is established. The algorithm is applicable in cases of multiple sources and/or targets. We give also here some ideas to adjust our algorithm to dynamic changes of arc capacities. For a graph of n nodes and m arcs, our algorithm takes O(n 2 m) message complexity and O(n 2) time complexity.