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Counting Homomorphic Cycles in Degenerate Graphs
Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that of graphs of ...
Approximating (k,ℓ)-Median Clustering for Polygonal Curves
In 2015, Driemel, Krivošija, and Sohler introduced the k,ℓ-median clustering problem for polygonal curves under the Fréchet distance. Given a set of input curves, the problem asks to find k median curves of at most ℓ vertices each that minimize the sum of ...
Ranked Document Retrieval in External Memory
The ranked (or top-k) document retrieval problem is defined as follows: preprocess a collection {T1,T2,… ,Td} of d strings (called documents) of total length n into a data structure, such that for any given query (P,k), where P is a string (called pattern)...
Monotone Edge Flips to an Orientation of Maximum Edge-Connectivity à la Nash-Williams
- Takehiro Ito,
- Yuni Iwamasa,
- Naonori Kakimura,
- Naoyuki Kamiyama,
- Yusuke Kobayashi,
- Shun-Ichi Maezawa,
- Yuta Nozaki,
- Yoshio Okamoto,
- Kenta Ozeki
We initiate the study of k-edge-connected orientations of undirected graphs through edge flips for k ≥ 2. We prove that in every orientation of an undirected 2k-edge-connected graph, there exists a sequence of edges such that flipping their directions one ...
Reliable Spanners for Metric Spaces
A spanner is reliable if it can withstand large, catastrophic failures in the network. More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation. In other words, the spanner property is ...
Competitive Algorithms for Generalized k-Server in Uniform Metrics
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server si lies in its own metric space Mi. A request is a k-tuple r = (r1,r2,… ,rk, which is served by moving some server si to the ...