Adam Karczmarz

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We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph G on n vertices can be partitioned into a set of O(n/r) edge-disjoint regions (called an r-division) with O(r) vertices each, such that each region has O( √ r) vertices (called boundary vertices) in common with other regions. A dense distance graph of a(More)
In this paper we study the problem of answering connectivity queries about a graph timeline. A graph timeline is a sequence of undirected graphs G1, . . . , Gt on a common set of vertices of size n such that each graph is obtained from the previous one by an addition or a deletion of a single edge. We present data structures, which preprocess the timeline(More)
A mergeable dictionary is a data structure storing a dynamic subset S of a totally ordered set U and supporting predecessor searches in S. Apart from insertions and deletions to S, we can both merge two arbitrarily interleaved dictionaries and split a given dictionary around some pivot x ∈ U . We present an implementation of a mergeable dictionary matching(More)
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in <i>O</i>(<i>n</i>log<sup>2</sup><i>n</i>loglog<i>n</i>) total time and explicitly maintains the set of vertices reachable from a fixed source vertex. Hence, if all edges are eventually(More)
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges. By applying the data structure, we can achieve optimal running times for(More)
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: • concat – concatenates two strings, • split – splits a string into two at a given position, • compare – finds the lexicographical order (less, equal, greater) between two strings, • LCP – calculates the longest common prefix of two(More)
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