The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure

Updating Recursive XML Views of Relations

This paper investigates the view update problem for XML views published from relational data. We consider XML views defined in terms of mappings directed by possibly recursive DTDs, compressed into DAGs and stored in relations. We provide new techniques to efficiently support XML view updates specified in terms of XPath expressions with recursion and complex filters. The interaction between XPath recursion and DAG compression of XML views makes the analysis of XML view updates rather intriguing. In addition, many issues are still open even for relational view updates, and need to be explored. In response to these, on the XML side, we revise the notion of side effects and update semantics based on the semantics of XML views, and present efficient algorithms to translate XML updates to relational view updates. On the relational side, we propose a mild condition on SPJ views, and show that under this condition the analysis of deletions on relational views becomes PTIME while the insertion analysis is NP-complete. We develop an efficient algorithm to process relational view deletions, and a heuristic algorithm to handle view insertions. Finally, we present an experimental study to verify the effectiveness of our techniques. 1

On the desirability and limitations of linear spatial database models

A general linear spatial database model is presented in which both the representation and the manipulation of non-spatial data is based on first-order logic over the real numbers with addition. We first argue the naturalness of our model and propose it as a general framework to study and compare linear spatial database models. However, we also establish that no reasonable safe extension of our data manipulation language can be complete for the linear spatial queries in that even very simple queries such as deciding colinearity or computing convex hull of a finite set of points cannot be expressed. We show that this fundamental result has serious ramifications for the way in which query languages for linear spatial database models have to be designed

Inherent Complexity of Recursive Queries

AbstractWe give lower bounds on the complexity of certain Datalog queries. Our notion of complexity applies to compile-time optimization techniques for Datalog; thus, our results indicate limitations of these techniques. The main new tool is linear first-order formulas, whose depth (respectively, number of variables) matches the sequential (respectively, parallel) complexity of Datalog programs. We define a combinatorial game (a variant of Ehrenfeucht–Fraı̈ssé games) that can be used to prove nonexpressibility by linear formulas. We thus obtain lower bounds for the sequential and parallel complexity of Datalog queries. We prove syntactically tight versions of our results, by exploiting uniformity and invariance properties of Datalog queries

Translating Updates of Relational Database Views

We study the problem of translating updates of data base views. We disambiguate a view update by requiring that a specified view compliment (i.e. a second view which contains all the data base information omitted from the given view) remains constant during the translation. We study some of the computational problems related to the application of this general methodology in the context of relational databases

The Complexity of Evaluation Relational Queries

We show that, given a relation R, a relational query ? Involving only projection and join, and a conjectured result r, resting with ?(R)=r is D^p complete. Bounding the size of ?(R) from below (above) is NP-hard (co-NP-hard), and bounding it both ways is D^p hard. Computing the size of ?(R) is #P-hard. We also show that, given two relations R1 and R2 and two queries ?1 and ?2 as above, testing whether ?1)R1)⊆?2(R2) and testing whether ?1(R1)=?2(R2) and both ∏p2-complete, even when R1-R2 or when ?1=?2

Equational theories and database constraints

The implication problem for database constraints is central in the fields of automated schema design and query optimization and has been traditionally approached with resolution-based techniques. We present a novel approach to database constraints, using equations instead of Horn clauses