arXiv subjects

Songyu Liu

Publications and source records attributed to Songyu Liu.

3 recordsLinked to original sources

arXiv2026

Layer-Respecting Linear Graph Layouts

We show how to visualize a graph, $G=(V,E)$, as a layered drawing, layer-respecting arc diagram, or layer-respecting linear cylindric drawing with a minimum number of edge crossings, where layer-respecting means that layers appear in order on a single line and vertices are grouped by their layers. Even though this problem is NP-hard for general arc diagrams, we show how to create such diagrams with fixed-parameter tractable linear-time algorithms, where the parameter that allows this is the width of a layered graph. Such a layered graph can be obtained from a breadth-first search (BFS), in which case the width is upper bounded by a graph width parameter called the BFS width.

cs.DS↗

arXiv2025

Exact Learning of Weighted Graphs Using Composite Queries

In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, $V$, of a weighted graph, $G=(V,E,w)$, but we are not given $E$. The problem, which is also known as graph reconstruction, is to determine all the edges of $E$, including their weights, by asking queries about $G$ from an oracle. As we observe, using simple shortest-path length queries is not sufficient, in general, to learn a weighted graph. So we study a number of scenarios where it is possible to learn $G$ using a subquadratic number of composite queries, which combine two or three simple queries.

cs.DS↗

arXiv2025

Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing

We provide the first approximation quality guarantees for the Cuthull-McKee heuristic for reordering symmetric matrices to have low bandwidth, and we provide an algorithm for reconstructing bounded-bandwidth graphs from distance oracles with near-linear query complexity. To prove these results we introduce a new width parameter, BFS width, and we prove polylogarithmic upper and lower bounds on the BFS width of graphs of bounded bandwidth. Unlike other width parameters, such as bandwidth, pathwidth, and treewidth, BFS width can easily be computed in polynomial time. Bounded BFS width implies bounded bandwidth, pathwidth, and treewidth, which in turn imply fixed-parameter tractable algorithms for many problems that are NP-hard for general graphs. In addition to their applications to matrix ordering, we also provide applications of BFS width to graph reconstruction, to reconstruct graphs from distance queries, and graph drawing, to construct arc diagrams of small height.

cs.DS↗