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Hidden Markov models (HMMs) and their variants were successfully used for several sequence annotation tasks. Traditionally, inference with HMMs is done using the Viterbi and posterior decoding algorithms. However, recently a variety of different optimization criteria and associated computational problems were proposed. In this paper, we consider three HMM decoding criteria and prove their NP hardness. These criteria consider the set of states used to generate a certain sequence, but abstract from the exact locations of regions emitted by individual states. We also illustrate experimentally that these criteria are useful for HIV recombination detection.
The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful Components
Let $G=(V,E)$ be an undirected graph with $n$ vertices and $m$ edges. We obtain the following new routing schemes: - A routing scheme for unweighted graphs that uses $tilde O(frac{1}{epsilon} n^{2/3})$ space at each vertex and $tilde O(1/epsilon)$-
Hidden Markov models are traditionally decoded by the Viterbi algorithm which finds the highest probability state path in the model. In recent years, several limitations of the Viterbi decoding have been demonstrated, and new algorithms have been dev
There has been a resurgence of interest in lower bounds whose truth rests on the conjectured hardness of well known computational problems. These conditional lower bounds have become important and popular due to the painfully slow progress on proving
Finding cohesive subgraphs in a network is a well-known problem in graph theory. Several alternative formulations of cohesive subgraph have been proposed, a notable example being $s$-club, which is a subgraph where each vertex is at distance at most