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)
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 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)
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 $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of vertices reachable from a fixed source vertex. Hence, if all edges are eventually deleted, the amortized time of(More)
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