A Pragmatic Non-blocking Concurrent Directed Acyclic Graph

Abstract

In this paper, we have developed two algorithms for maintaining acyclicity in a concurrent directed graph. The first algorithm is based on a wait-free reachability query and the second one is based on partial snapshot-based obstruction-free reachability query. Interestingly, we are able to achieve the acyclic property in the dynamic setting without the need of helping using descriptors by other threads or clean double collect mechanism. We present a proof to show that the graph remains acyclic at all times in the concurrent setting. We also prove that the acyclic graph data-structure operations are linearizable. We implement both the algorithms in C++ and test through a number of micro-benchmarks. Our experimental results show an average of 7x improvement over the sequential and global lock implementation.keywords: acyclic graph concurrent data structure linearizability lock-freedom.arXiv:1611.03947v6 [cs.DC] 12 May 20191. We describe an Abstract Data Type (ADT) that maintains an acyclic directed graph G = (V, E). It comprises of the following operations on the sets V and E: (1) Add Vertex:AcyAddV (2) Remove Vertex: AcyRemV, (3) Contains Vertex: AcyConV (4) Add Edge: AcyAddE (5) Remove Edge: AcyRemE and (6) Contains Edge: AcyConE. The ADT remains acyclic after completion of any of the above operations in G. The acyclic graph is represented as an adjacency list like in [4].2. We present an efficient concurrent non-blocking implementation of the ADT (Section 3). We present two approaches for maintaining acyclicity: the first one is based on a wait-free reachability query and the second one is based on obstruction-free reachability query similar to the GetPath operation of Chatterjee et al.[4] (Section 4).3. We prove the correctness by showing the operations of the concurrent acyclic graph datastructure are linearizable [10]. We also prove the non-blocking progress guarantee: (a) The operations AcyConV and AcyConE are wait-free, only if the vertex keys are finite; (b) Among the two algorithms for maintaining acyclicity, we show that the first algorithm based on searchability is wait-free, whereas the second algorithm based on reachability queries is obstruction-free and (c) The operations AcyAddV, AcyRemV, AcyConV, AcyAddE, AcyRemE, and AcyConE are lock-free. Section 5.4. We evaluated the non-blocking algorithms in C++ implementation and tested through a number of micro-benchmarks. Our experimental results depict on an average of 7x improvement over the sequential and global lock implementation (Section 6).

Building Efficient Concurrent Graph Object through Composition of List-based Set

“…a The complete source code is available on Github [9]. In the experiments conducted, we start with an initial complete graph.…”