A linear time algorithm for Shortest Cyclic Cover of Strings

A linear time algorithm for Shortest Cyclic Cover of Strings

Merging words according to their overlap yields a superstring. This basic operation allows to infer long strings from a collection of short pieces, as in genome assembly. To capture a maximum of overlaps, the goal is to infer the shortest superstring of a set of input words. The Shortest Cyclic Cover of Strings (SCCS) problem asks, instead of a single linear superstring, for a set of cyclic str...

A Linear-Time Parameterized Algorithm for Node Unique Label Cover

The optimization version of the Unique Label Cover problem is at the heart of the Unique Games Conjecture which has played an important role in the proof of several tight inapproximability results. In recent years, this problem has been also studied extensively from the point of view of parameterized complexity. Chitnis et al. [FOCS 2012, SICOMP 2016] proved that this problem is fixed-parameter...

A Practical Shortest Path Algorithm with Linear Expected Time

A Simple Shortest Path Algorithm with Linear Average Time

We present a simple shortest path algorithm. If the input lengths are positive and uniformly distributed, the algorithm runs in linear time. The worst-case running time of the algorithm is O(m + n logC), where n and m are the number of vertices and arcs of the input graph, respectively, and C is the ratio of the largest and the smallest nonzero arc length.

A Linear-Time and Linear-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

In this paper, we develop the message passing based lineartime and linear-space MVC algorithm (MVC-MPL) for solving the minimum vertex cover (MVC) problem. MVC-MPL is based on heuristics derived from a theoretical analysis of message passing algorithms in the context of belief propagation. We show that MVC-MPL produces smaller vertex covers than other linear-time and linear-space algorithms. In...