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We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This speedup is obtained through the use of dense distance graphs combined with a divide-and-conquer approach.

Let G = (V, E) be a planar n-vertex digraph. Consider the problem of computing max st-flow values in G from a fixed source s to all sinks t ∈ V \ {s}. We show how to solve this problem in near-linear O(n log 3 n) time. Previously, no better solution was known than running a single-source single-sink max flow algorithm n−1 times, giving a total time bound of… (More)

- Jakub Lacki
- SODA
- 2011

This paper presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in <i>O</i>(<i>mn</i>) time and answers queries in constant time. Until now such time bound has only been achieved by a randomized Las Vegas algorithm.
In addition to that, a few… (More)

It was experimentally observed that the majority of real-world networks are scale-free and follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such " typical " networks. The contribution of this work is twofold. First, we define a deterministic condition for checking whether a graph has a power law degree… (More)

This article presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in <i>O</i>(<i>mn</i>) time and answers queries in constant time. Previously, such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a… (More)

In this paper we consider the problem of maintaining information about graphs with history -- so called <i>graph timeline</i>. A graph timeline is a sequence of graphs G<sub>1</sub>,..., G<sub>t</sub>, in which consecutive graphs are obtained from previous ones by small modifications, e.g., by adding or removing a single edge. We aim to devise algorithms… (More)

We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth k, we present two improved static algorithms for both the problems that run in time O(n · k 2.38 · 2 k) and O(m · log n · k),… (More)

BACKGROUND
Constraint-based approaches facilitate the prediction of cellular metabolic capabilities, based, in turn on predictions of the repertoire of enzymes encoded in the genome. Recently, genome annotations have been used to reconstruct genome scale metabolic reaction networks for numerous species, including Homo sapiens, which allow simulations that… (More)

We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form “Are vertices u and v connected with a path?" in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in… (More)

We review the history of the road to a manifestly covariant per-turbative calculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We chose as our case study the calculation of the cross-section of the Compton effect. We analyse Stueckelberg's paper extensively. This… (More)