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Scene Grammars, Factor Graphs, and Belief Propagation
We describe a general framework for probabilistic modeling of complex scenes and for inference from ambiguous observations. The approach is motivated by applications in image analysis and is based on the use of priors defined by stochastic grammars. We ...
Embeddability in R3 is NP-hard
We prove that the problem of deciding whether a two- or three-dimensional simplicial complex embeds into R3 is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an S3 filling is NP-hard. The former stands ...
Planar Graph Perfect Matching Is in NC
Is perfect matching in NC? That is, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC perfect matching algorithms. ...
Planar Graphs Have Bounded Queue-Number
We show that planar graphs have bounded queue-number, thus proving a conjecture of Heath et al. [66] from 1992. The key to the proof is a new structural tool called layered partitions, and the result that every planar graph has a vertex-partition and a ...
The Log-Approximate-Rank Conjecture Is False
We construct a simple and total Boolean function F = f ○ XOR on 2n variables that has only O(√n) spectral norm, O(n2) approximate rank, and O(n2.5) approximate nonnegative rank. We show it has polynomially large randomized bounded-error communication ...
A Simple and Approximately Optimal Mechanism for an Additive Buyer
We consider a monopolist seller with n heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The seller aims to ...
Forcing and Calculi for Hybrid Logics
The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics ...
