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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 &#x03F5; V \ {s}. We show how to solve this problem in near-linear O(n log<sup>3</sup> n) time. Previously, nothing better was known than running a single-source singlesink max How algorithm n-1 times, giving a total(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 paper presents a new deterministic algorithm for decre-mental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) 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 decremental(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)
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)
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 provide(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 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)
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an n-vertex graph G=(V,E,w) with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set S &#8838; V, which changes over time. The changes applied(More)