18 research outputs found
CORAE: A Tool for Intuitive and Continuous Retrospective Evaluation of Interactions
This paper introduces CORAE, a novel web-based open-source tool for
COntinuous Retrospective Affect Evaluation, designed to capture continuous
affect data about interpersonal perceptions in dyadic interactions. Grounded in
behavioral ecology perspectives of emotion, this approach replaces valence as
the relevant rating dimension with approach and withdrawal, reflecting the
degree to which behavior is perceived as increasing or decreasing social
distance. We conducted a study to experimentally validate the efficacy of our
platform with 24 participants. The tool's effectiveness was tested in the
context of dyadic negotiation, revealing insights about how interpersonal
dynamics evolve over time. We find that the continuous affect rating method is
consistent with individuals' perception of the overall interaction. This paper
contributes to the growing body of research on affective computing and offers a
valuable tool for researchers interested in investigating the temporal dynamics
of affect and emotion in social interactions
On the Complexity of Searching in Trees: Average-case Minimization
We focus on the average-case analysis: A function w : V -> Z+ is given which
defines the likelihood for a node to be the one marked, and we want the
strategy that minimizes the expected number of queries. Prior to this paper,
very little was known about this natural question and the complexity of the
problem had remained so far an open question.
We close this question and prove that the above tree search problem is
NP-complete even for the class of trees with diameter at most 4. This results
in a complete characterization of the complexity of the problem with respect to
the diameter size. In fact, for diameter not larger than 3 the problem can be
shown to be polynomially solvable using a dynamic programming approach.
In addition we prove that the problem is NP-complete even for the class of
trees of maximum degree at most 16. To the best of our knowledge, the only
known result in this direction is that the tree search problem is solvable in
O(|V| log|V|) time for trees with degree at most 2 (paths).
We match the above complexity results with a tight algorithmic analysis. We
first show that a natural greedy algorithm attains a 2-approximation.
Furthermore, for the bounded degree instances, we show that any optimal
strategy (i.e., one that minimizes the expected number of queries) performs at
most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is
the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum
degree of T. We combine this result with a non-trivial exponential time
algorithm to provide an FPTAS for trees with bounded degree
Binary Identification Problems for Weighted Trees
The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a node in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T − e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. More- over, for the degree 2 case, we significantly improve the straightforward O(n^3) dynamic programming approach, and provide an O(n^2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn
The Binary Identification Problems for Weighted Trees
The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a vertex in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T − e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. Moreover, for the degree 2 case, we significantly improve the straightforward O(n^3) dynamic programming approach, and provide an O(n^2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn