Optimal Coalition Structures in Cooperative Graph Games

Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation [14], which maintains knowledge about synergies between agents in the form of an edge weighted graph. We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that finding the optimal coalition structure is not only hard for general graphs, but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems. We then provide algorithms with constant factor approximations for planar, minor-free and bounded degree graphs.Comment: 16 pages. A short version of this paper is to appear at AAAI 201

Sketch recognition of digital ink diagrams : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science at Massey University, Palmerston North, New Zealand

Figures are either re-used with permission, or abstracted with permission from the source article.Sketch recognition of digital ink diagrams is the process of automatically identifying hand-drawn elements in a diagram. This research focuses on the simultaneous grouping and recognition of shapes in digital ink diagrams. In order to recognise a shape, we need to group strokes belonging to a shape, however, strokes cannot be grouped until the shape is identified. Therefore, we treat grouping and recognition as a simultaneous task. Our grouping technique uses spatial proximity to hypothesise shape candidates. Many of the hypothesised shape candidates are invalid, therefore we need a way to reject them. We present a novel rejection technique based on novelty detection. The rejection method uses proximity measures to validate a shape candidate. In addition, we investigate on improving the accuracy of the current shape recogniser by adding extra features. We also present a novel connector recognition system that localises connector heads around recognised shapes. We perform a full comparative study on two datasets. The results show that our approach is significantly more accurate in finding shapes and faster on process diagram compared to Stahovich et al. (2014), which the results show the superiority of our approach in terms of computation time and accuracy. Furthermore, we evaluate our system on two public datasets and compare our results with other approaches reported in the literature that have used these dataset. The results show that our approach is more accurate in finding and recognising the shapes in the FC dataset (by finding and recognising 91.7% of the shapes) compared to the reported results in the literature

A Graphical Model for Simultaneous Partitioning and Labeling

In this work we develop a graphical model for describing probability distributions over labeled partitions of an undirected graph which are conditioned on observed data. We show how to efficiently perform exact inference in these models, by exploiting the structure of the graph and adapting the sum-product and max-product algorithms. We demonstrate our approach on the task of segmenting and labeling hand-drawn ink fragments, and show that a significant performance increase is obtained by labeling and partitioning simultaneously.

A Graphical Model for Simultaneous Partitioning and Labeling

In this work we develop a graphical model for describing probability distributions over labeled partitions of an undirected graph which are conditioned on observed data. We show how to efficiently perform exact inference in these models, by exploiting the structure of the graph and adapting the sum-product and max-product algorithms. We demonstrate our approach on the task of segmenting and labeling hand-drawn ink fragments, and show that a significant performance increase is obtained by labeling and partitioning simultaneously