Vijay Raghavan

Scalar aggregation in inconsistent databases

We consider here scalar aggregation queries in databases that may violate a given set of functional dependencies. We define consistent answers to such queries to be greatest-lowest/least-upper bounds on the value of the scalar function across all (minimal) repairs of the database. We show how to compute such answers. We provide a complete characterization of the computational complexity of this problem. We also show how tractability can be improved in several special cases (one involves a novel application of Boyce-Codd Normal Form) and present a practical hybrid query evaluation method.

How many queries are needed to learn

We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any “honest” class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P = NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Γ p 4 .

Robust algorithms for restricted domains

We introduce a new definition of efficient algorithms for restricted domains. Under this definition, an algorithm is required to be “robust,” i.e., it must produce correct output regardless of whether the input actually belongs to the restricted domain or not. This is to be contrasted with the “promise” version of solving problems on restricted domains, in which there is a guarantee that the input is in the class, and an algorithm to “solve” the problem need not function correctly or even terminate if this guarantee is not met. The more stringent requirement of robustness in algorithms gives an important benefit: such algorithms are amenable to manipulation as building blocks of more general algorithms; in other words, composition of robust algorithms preserves robustness. In contrast, promise algorithms cannot be so composed. There exist problems which have a polynomial time promise solution, while being NP-hard if required to be robust. We show the perhaps surprising result that finding a maximum independent set in a well-covered graph (i.e., a graph in which every maximal independent set is of the same size) is NP-hard. An argument can be made that this hardness result is more meaningful than the trivial polynomial time promise algorithm. Graph classes provide interesting natural restricted domains; there are many problems which are efficiently solvable given a special and natural representation of a graph (i.e., a “model”), but which are open with respect to time complexity if the graph is given in a general form such as an adjacency list or an adjacency matrix. One such open problem is that of finding a maximum clique in unit disk graphs here, we give a polynomial time robust algorithm for this problem, i.e., given an input graph G in general form, the output is either a maximum clique for G or a certificate that G is not a unit disk graph. The existence of this algorithm is to be reconciled with the apparent contradiction posed by the facts:Recognizing whether an input graph given in general form is a unit disk graph is NP-hard; in fact, it is not even known to be in NP. Finding a maximum clique in an input graph given in general form is NP-hard.

Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number

Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more efficiently than by using the well-known algorithms based on bipartite matching and matrix multiplication. In particular, we show that deciding deciding if an order has width k can be done in O(kn2) time and whether a graph has Dilworth number k can be done in O(k2n2) time.For very small k we have even better results. We show that orders of width at most 3 can be recognized in O(n) time and of width at most 4 in O(nlog n).

On the limits of proper learnability of subclasses of DNF formulas

Bshouty, Goldman, Hancock and Matar have shown that up to log n-term DNF formulas can be properly learned in the exact model with equivalence and membership queries. Given standard complexity-theoretical assumptions, we show that this positive result for proper learning cannot be significantly improved in the exact model or the PAC model extended to allow membership queries. Our negative results are derived from two general techniques for proving such results in the exact model and the extended PAC model. As a further application of these techniques, we consider read-thrice DNF formulas. Here we improve on Aizenstein, Hellerstein, and Pitts negative result for proper learning in the exact model in two ways. First, we show that their assumption of NP ≠ co-NP can be replaced with the weaker assumption of P ≠ NP. Second, we show that read-thrice DNF formulas are not properly learnable in the extended PAC model, assuming RP ≠ NP.

Atropisomeric Dihydroanthracenones as Inhibitors of Multiresistant Staphylococcus aureus

Two bisdihydroanthracenone atropodiastereomeric pairs, including homodimeric flavomannin A (1) and the previously unreported flavomannin B (2), two new unsymmetrical dimers (3 and 4), and two new mixed dihydroanthracenone/anthraquinone dimers (5 and 6) were isolated from Talaromyces wortmannii , an endophyte of Aloe vera . The structures of 2-6 were elucidated by extensive NMR and mass spectrometric analyses. The axial chirality of the biaryls was determined using TDDFT ECD and VCD calculations, the combination of which however did not allow the assignment of the central chirality elements of 1. The compounds exhibited antibacterial activity against Staphylococcus aureus , including (multi)drug-resistant clinical isolates. Reporter gene analyses indicated induction of the SOS response for some of the derivatives, suggesting interference with DNA structure or metabolism. Fluorescence microscopy demonstrated defective segregation of the bacterial chromosome and DNA degradation. Notably, the compounds showed no cytotoxic activity, encouraging their further evaluation as potential starting points for antibacterial drug development.

Read-Twice DNF Formulas Are Properly Learnable

We show that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time. Our algorithm uses membership queries and proper equivalence queries and is based on a simple, new characterization of minimal read-twice DNF formulas. The algorithm improves on earlier results of Hancock and Aizenstein and Pitt which showed that read-twice DNF formulas are learnable using more powerful equivalence queries, i.e., where the hypotheses could be arbitrary DNF formulas. We also improve on the time-complexity of these earlier algorithms. Other results which may be of independent interest outside of learning follow directly from this paper. Specifically, we show that read-twice DNF formulas can be tested for equivalence in polynomial time and that the smallest read-twice formula equivalent to a given one can be found in polynomial time.

Sequential diagnosability is co-NP complete

F.P. Preparata et al. (1967) introduced a graph-theoretical model for fault diagnosis called the PMC model. The question of determining the sequential diagnosability number of a system in the PMC model has remained open. The authors formalize the notion of sequential diagnosability. The question of determining the sequential diagnosability number of a system is addressed by showing that the appropriate decision problem is co-NP complete. The problem is also shown to be co-NP complete even when restricted to planar graphs both in the weighted and the BGM models. >

Learning μ-branching programs with queries

We show that the class of p-branching programs can be exactly learned in ()(rz5) time us:n

Exact learning of DNF formulas using DNF hypotheses

only O(n) equivalence queries and O(n ) membership queries, but neither type of query alone is sufficient for polynomial time learning.