We present a prototype online system to automate the procedure of computing different types of linear layouts of graphs under different user-specific constraints. The system consists of two main components; the client and the server sides. The client side is built upon an easy-to-use editor, which supports basic interaction with graphs, enriched with several additional features to allow the user to define and further constraint the linear layout to be computed. The server side, which is available to multiple clients through a well-documented API, is responsible for the actual computation of the linear layout. Its algorithmic core is an extension of a SAT formulation that is known to be robust enough to solve non-trivial instances in reasonable amount of time. However, it has also several known limitations and potential improvements that~we address in this work (e.g., limited applicability to a particular type of linear layouts, no support for additional constraints, limited extendability e.t.c.). As a proof of concept, we present our findings for a sketch of a proof of an important result in the field that was proposed by Yannakakis back in 1986 (whose details, however, have not been published so far).

中文翻译：

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用于交互和有效计算图形线性布局的在线框架

我们提出了一个原型在线系统，以在不同的用户特定约束下自动计算不同类型的图形线性布局的过程。该系统由两个主要部分组成；客户端和服务器端。客户端建立在一个易于使用的编辑器上，它支持与图形的基本交互，丰富了几个附加功能，允许用户定义和进一步约束要计算的线性布局。服务器端通过一个文档齐全的 API 可供多个客户端使用，负责线性布局的实际计算。它的算法核心是 SAT 公式的扩展，众所周知，该公式足够健壮，可以在合理的时间内解决非平凡的实例。然而，它也有几个已知的限制和潜在的改进~我们在这项工作中解决（例如，对特定类型的线性布局的适用性有限，不支持额外的约束，有限的可扩展性等）。作为概念证明，我们展示了我们的研究结果，该结果是由 Yannakakis 在 1986 年提出的该领域重要结果的证明草图（然而，其细节目前尚未公布）。