Related papers: (Quasi-)linear time algorithm to compute LexDFS, L…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…
We present the first linear-time algorithm that computes the $4$-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing $4$-edge connectivity. Our results are based on a…
We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose,…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…
It is shown that a breadth-first search in a directed or undirected graph with $n$ vertices and $m$ edges can be carried out in $O(n+m)$ time with $n\log_2 3+O((\log n)^2)$ bits of working memory.
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for the efficient implementation of DFS-based graph algorithms and exemplify them on three algorithms for computing strongly…
A linear time algorithm to find a set of nearest elements in a mesh.
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We show how to solve directed Laplacian systems in nearly-linear time. Given a linear system in an $n \times n$ Eulerian directed Laplacian with $m$ nonzero entries, we show how to compute an $\epsilon$-approximate solution in time $O(m…
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…
Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be reordered. We present a new polynomial time algorithm to…
To determine that two given undirected graphs are isomorphic, we construct for them auxiliary graphs, using the breadth-first search. This makes capability to position vertices in each digraph with respect to each other. If the given graphs…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…