In this paper, we show that in a parallel processing system, if a directed acyclic graph (DAG) can be induced in the state space and execution is \textit{enforced} along that DAG, then synchronization cost can be eliminated. Specifically, we show that in such systems, correctness is preserved even if the nodes execute asynchronously and rely on old/inconsistent information of other nodes. We present two variations for inducing DAGs -- \textit{DAG-inducing problems}, where the problem definition itself induces a DAG, and \textit{DAG-inducing algorithms}, where a DAG is induced by the algorithm. We demonstrate that the dominant clique (DC) problem and shortest path (SP) problem are DAG-inducing problems. Among these, DC allows self-stabilization, whereas the algorithm that we present for SP does not. We demonstrate that maximal matching (MM) and 2-approximation vertex cover (VC) are not DAG-inducing problems. However, DAG-inducing algorithms can be developed for them. Among these, the algorithm for MM allows self-stabilization and the 2-approx. algorithm for VC does not. Our algorithm for MM converges in $2n$ moves and does not require a synchronous environment, which is an improvement over the existing algorithms in the literature. Algorithms for DC, SP and 2-approx. VC converge in $2m$, $2m$ and $n$ moves respectively. We also note that DAG-inducing problems are more general than, and encapsulate, lattice linear problems (Garg, SPAA 2020). Similarly, DAG-inducing algorithms encapsulate lattice linear algorithms (Gupta and Kulkarni, SSS 2022).

翻译：本文表明，在并行处理系统中，若其状态空间可诱导出有向无环图（DAG）且执行过程沿该DAG方向强制推进，则同步开销可被消除。具体而言，我们证明在此类系统中，即使节点异步执行并依赖其他节点的过时/不一致信息，系统正确性仍能得以保持。我们提出两种DAG诱导变体——DAG诱导问题（问题定义本身诱导出DAG）与DAG诱导算法（算法诱导出DAG）。我们证明主团（DC）问题与最短路径（SP）问题属于DAG诱导问题。其中，DC问题可实现自稳定，而本文提出的SP算法不具备自稳定性。我们证明最大匹配（MM）问题和2-近似顶点覆盖（VC）问题并非DAG诱导问题，但可为其设计DAG诱导算法。其中，MM算法具备自稳定性，而2-近似VC算法不具备。本文MM算法在$2n$步内收敛且无需同步环境，相较于现有文献中的算法有所改进。DC、SP和2-近似VC算法分别可在$2m$、$2m$和$n$步内收敛。我们还指出，DAG诱导问题比格点线性问题（Garg，SPAA 2020）更具一般性并涵盖后者，类似地，DAG诱导算法也涵盖格点线性算法（Gupta和Kulkarni，SSS 2022）。