8456161
Negation as Failure as Resolution
Providing a clean procedural semantics of the “Negation As Failure rule” in Logic Programming has been an open problem for some time now. This rule has been treated as a technique in nonmonotonic reasoning, not as a rule in classical logic. This paper contains a demonstration of the negation as failure rule as a resolution procedure in first-order logic. We present a sound and complete resolution scheme for negation as failure rule for the larger class of constraint logic programs. The approach is to consider a canonical partition of the completion of a definite (constraint) program into the IF and the FI programs. We show that a negated goal, provable from the completed definite program is provable from just the FI part. The clauses in this program have a structure dual to that of definite Horn clauses. We describe a sound and complete linear resolution rule for this fragment, and show that a resolution proof of the negated goal from the FI part corresponds to a finite failure tree resulting from classical linear resolution applied to the goal on the If part of the original definite program. Our work shows that negation as failure rule can be computationally efficient in the sense that the SLD-resolution on the If part of a definite program along with the negation as failure rule is more efficient than a direct resolution procedure on the completion of that program.
37032385
Completeness of neighbourhood logic
12929901
Completeness of Neighbourhood Logic
This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities. NL can support the specification of liveness and fairness properties of computing systems as well as formalisation of many concepts of real analysis. These two modalities are also adequate in the sense that they can derive other important unary and binary modalities of interval temporal logic. We prove the completeness result for NL by giving a Kripke model semantics and then mapping the Kripke models to the interval models for NL.
5884615
The Directed Planar Reachability Problem
We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case. 
 
We also consider a previously-studied subclass of planar graphs known as grid graphs. We show that the directed planar s-t-connectivity problem reduces to the reachability problem for directed grid graphs. 
 
A special case of the grid-graph reachability problem where no edges are directed from right to left is known as the “layered grid graph reachability problem”. We show that this problem lies in the complexity class UL.
11274155
Minimum-Energy Broadcast Using Practical Directional Antennas in All-Wireless Networks
Energy-efficient broadcast communication is an important problem in wireless ad hoc networks. Previously, minimum-energy broadcast that exploits the broadcast nature of radio transmission has been studied and shown to be NP-complete for omnidirectional antennas. In this paper, we investigate the minimum-energy broadcast problem under a wide spectrum of directional antenna models, including sectored antennas with fixed sectors and beamwidth and antenna array-based smart antennas with varying degrees of beam orientation and beamwidth. We first propose the RF design and implementation of each model, which suggests the practical parameters of antennas under that model. We then show that the minimum-energy broadcast problem under each of the antenna models is NP-complete. Lastly, we present a heuristic algorithm based on BIP for the above problem under each directional antenna model and experimentally compare the energy efficiency of using different directional antennas using these heuristics. Our results show that using antennas with adjustable orientation and variable beamwidth gives the best results. For such antennas, the scanning angle is the dominant factor in improving the quality of the broadcast trees. The number of antennas per node is not that critical to obtaining a better broadcast tree as long as it is large enough to cover the entire 360◦ around a node so as to prevent network partitioning.
54110472
Fast and Accurate Text Classification via Multiple Linear Discriminant Projections
Publisher Summary 
Text classification is a standard problem in information retrieval (IR). A learner is presented with training documents, each labeled as containing or not containing material relevant to a given topic. Support vector machines (SVMs) have shown superb performance for text classification tasks. They are accurate, robust, and quick to apply to test instances. Their only potential drawback is their training time and memory requirement. SVMs have been trained on data sets with several thousand instances, but Web directories today contain millions of instances that are valuable for mapping billions of Web pages into Yahoo!-like directories. This chapter presents Simple Iterative Multiple Projection on Lines (SIMPL), a nearly linear-time classification algorithm that mimics the strengths of SVMs while avoiding the training bottleneck. It uses Fisher's linear discriminant, a classical tool from statistical pattern recognition, to project training instances to a carefully selected low-dimensional subspace before inducing a decision tree on the projected instances. SIMPL uses efficient sequential scans and sorts, and is comparable in speed and memory scalability to widely used naive Bayes (NB) classifiers, but it beats NB accuracy decisively.
411400
Parity Problems in Planar Graphs
We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in the non-modular case, our problem is as hard in the planar case as for the case of arbitrary graphs. This completely settles the question regarding the complexity of modular computation of the number of spanning trees in planar graphs. The techniques used rely heavily on algebraic-topology. In the spirit of counting problems modulo 2k, we also exhibit a highly parallel oplusL algorithm for finding the value of a Permanent modulo 2k. Previously, the best known result in this direction was Valiant's result that this problem lies in P.
2157131
CONDENSATION-Based Predictive EigenTracking
An appearance-based EigenTracker can track objects which simultaneously undergo image motions as well as changes in view. This paper enhances the framework in two ways. First, we incorporate a novel CONDENSATION-based predictive framework to speed up the EigenTracker. Next, our scheme is on-line: we use efficient eigenspace updates to track unknown objects. We use Importance Sampling for enhancing the capability of an EigenTracker. Our on-line EigenTracker is flexible it is possible to use it in conjunction with other trackers in a symbiotic manner. We show results of efficient and successful tracking for two important applications – hand gesture analysis, and face and person tracking.