deletion number”, “vertex cover number”, and “feedback edge set number ” of the underlying graph on the problem’s complexity, revealing both tractable and intractable cases. For instance, even for diameter-two split graphs TSS remains very hard. TSS can be efficiently solved on graphs with small feedback

properties of the query hypergraph. For instance, acyclic queries can be answered in polynomial time, and also query containment is efficiently decidable for acyclic queries. In this report, we review both quantitative and structural methods for optimizing query answering and identifying tractable classes

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filter-ing, the belief state is a logical formula describing the pos-sible world states. Efficient algorithms for logical filtering bear important implications on reasoning tasks such as plan-ning and diagnosis. In this paper, we will identify classes of transition constraints that are amenable to compact and indefinite filtering—presenting efficient algorithms wherever necessary. We will first show that connected row-convex (CRC) constraints are amenable to efficient filtering when path-consistency is enforced in appropriate steps. We will then extend this theory to provide a filtering algorithm based on repeatedly enforcing path-consistency and embedding the domain values of the related variables in tree structures to guarantee global consistency. Finally, we will identify and comment on the problem of multi-agent localization as a po-tential application of the theory developed in the paper (under some reasonable assumptions).

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing the possible world states. Efficient algorithms for logical filtering bear important implications on reasoning tasks such as planning and diagnosis. In this paper, we will identify classes of transition constraints that are amenable to compact and indefinite filtering—presenting efficient algorithms wherever necessary. We will first show that connected row-convex (CRC) constraints are amenable to efficient filtering when path-consistency is enforced in appropriate steps. We will then extend this theory to provide a filtering algorithm based on repeatedly enforcing path-consistency and embedding the domain values of the related variables in tree structures to guarantee global consistency. Finally, we will identify and comment on the problem of multi-agent localization as a potential application of the theory developed in the paper (under some reasonable assumptions).

deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability results for the structuralmodel approach.

between EGC constraints and general factors in graphs. This allows us to extend the known polynomial-time case to certain non-interval cardinality sets. Second we consider EGC constraints under restrictions in terms of the treewidth of the value graph (the bipartite graph representing variable-value pairs

deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability results for the structural-model approach.

The Maximum Betweenness Centrality problem (MBC) can be defined as follows. Given a graph find a k-element node set C that maximizes the probability of detecting commu-nication between a pair of nodes s and t chosen uniformly at random. It is assumed that the communication between s and t is realized along a shortest s–t path which is, again, selected uniformly at random. The communication is detected if the communication path contains a node of C. Recently, Dolev et al. (2009) showed that MBC is NP-hard and gave a (1−1/e)-approximation using a greedy approach. We provide a reduction of MBC to Maximum Coverage that sim-plifies the analysis of the algorithm of Dolev et al. considerably. Our reduction allows us to obtain a new algorithm with the same approximation ratio for a (generalized) budgeted version of MBC. We provide tight examples showing that the analyses of both algorithms are best pos-sible. Moreover, we prove that MBC is APX-complete and provide an exact polynomial-time algorithm for MBC on tree graphs. 1

. We present new tractable cases for default reasoning from conditional knowledge bases. In detail, we introduce q-Horn conditional knowledge bases, which allow for a limited use of disjunction. We show that previous tractability results for "-entailment, proper "-entailment, and z

bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedback-free Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases