Combining Clickstream Analyses and Graph-Modeled Data Clustering for Identifying Common Response Processes.

Complex interactive test items are becoming more widely used in assessments. Being computer-administered, assessments using interactive items allow logging time-stamped action sequences. These sequences pose a rich source of information that may facilitate investigating how examinees approach an item and arrive at their given response.

Stable roommates with narcissistic, single-peaked, and single-crossing preferences.

The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e.

Parameterized Algorithmics for Finding Exact Solutions of NP-Hard Biological Problems.

Fixed-parameter algorithms are designed to efficiently find optimal solutions to some computationally hard (NP-hard) problems by identifying and exploiting "small" problem-specific parameters. We survey practical techniques to develop such algorithms. Each technique is introduced and supported by case studies of applications to biological problems, with additional pointers to experimental results.

Partitioning Biological Networks into Highly Connected Clusters with Maximum Edge Coverage.

A popular clustering algorithm for biological networks which was proposed by Hartuv and Shamir identifies nonoverlapping highly connected components. We extend the approach taken by this algorithm by introducing the combinatorial optimization problem Highly Connected Deletion, which asks for removing as few edges as possible from a graph such that the resulting graph consists of highly connected components. We show that Highly Connected Deletion is NP-hard and provide a fixed-parameter algorithm and a kernelization.

Parameterized algorithmics for finding connected motifs in biological networks.

We study the NP-hard LIST-COLORED GRAPH MOTIF problem which, given an undirected list-colored graph G = (V, E) and a multiset M of colors, asks for maximum-cardinality sets S ⊆ V and M' ⊆ M such that G[S] is connected and contains exactly (with respect to multiplicity) the colors in M'. LIST-COLORED GRAPH MOTIF has applications in the analysis of biological networks. We study LIST-COLORED GRAPH MOTIF with respect to three different parameterizations.

Developing fixed-parameter algorithms to solve combinatorially explosive biological problems.

Fixed-parameter algorithms can efficiently find optimal solutions to some computationally hard (NP-hard) problems. This chapter surveys five main practical techniques to develop such algorithms. Each technique is circumstantiated by case studies of applications to biological problems.

Breakpoint medians and breakpoint phylogenies: a fixed-parameter approach.

With breakpoint distance, the genome rearrangement field delivered one of the currently most popular measures in phylogenetic studies for related species. Here, BREAKPOINT MEDIAN, which is NP-complete already for three given species (whose genomes are represented as signed orderings), is the core basic problem. For the important special case of three species, approximation (ratio 7/6) and exact heuristic algorithms were developed.