12753612
The well-founded semantics for general logic programs
A general logic program (abbreviated to "program" hereafter) is a set of roles that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) slttmg above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program, " or Its "declarative semantics. " Ideally, queries directed to the program would be answered in accordance with this model. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. Unfounded sets and well-founded partial models are introduced and the well-founded semantics of a program are defined to be its well-founded partial model. If the well-founded partial model is m fact a total model. it is called the well-founded model. It n shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, The method in this paper is also compared with other proposals in the literature, including Clark's "program completion, " Fitting's and Kunen's 3-vahred interpretations of it, and the "stable models" of Gelfond and Lifschitz.
9401708
Complex Aggregation at Multiple Granularities
Datacube queries compute simple aggregates at multiple granularities. In this paper we examine the more general and useful problem of computing a complex subquery involving multiple dependent aggregates at multiple granularities. We call such queries multi-feature cubes. An example is Broken down by all combinations of month and customer, find the fraction of the total sales in 1996 of a particular item due to suppliers supplying within 10% of the minimum price (within the group), showing all subtotals across each dimension. We classify multi-feature cubes based on the extent to which fine granularity results can be used to compute coarse granularity results; this classification includes distributive, algebraic and holistic multi-feature cubes. We provide syntactic sufficient conditions to determine when a multi-feature cube is either distributive or algebraic. This distinction is important because, as we show, existing datacube evaluation algorithms can be used to compute multi-feature cubes that are distributive or algebraic, without any increase in I/O complexity. We evaluate the CPU performance of computing multi-feature cubes using the datacube evaluation algorithm of Ross and Srivastava. Using a variety of synthetic, benchmark and real-world data sets, we demonstrate that the CPU cost of evaluating distributive multi-feature cubes is comparable to that of evaluating simple datacubes. We also show that a variety of holistic multi-feature cubes can be evaluated with a manageable overhead compared to the distributive case.
7567374
Foundations of Aggregation Constraints
We introduce a new constraint domain, aggregation constraints, which is useful in database query languages, and in constraint logic programming languages that incorporate aggregate functions. We study the fundamental problem of checking if a conjunction of aggregation constraints is solvable, and present undecidability results for many different classes of aggregation constraints. We describe a complete and minimal axiomatization of the class of aggregation constraints over finite multisets of reals, which permits a natural reduction from the class of aggregation constraints to the class of mixed integer/real, non-linear arithmetic constraints. We then present a polynomial-time algorithm that directly checks for solvability of a useful class of aggregation constraints, where the reduction-based approach does not lead to efficient checks for solvability.
16656102
Groupwise Processing of Relational Queries
In this paper, we define and examine a particular class of queries called group queries. Group queries are natural queries in many decisionsupport applications. The main characteristic of a group query is that it can be executed in a groupby-group fashion. In other words, the underlying relation(s) can be partitioned (based on some set of attributes) into disjoint groups, and each group can be processed separately. We give a syntactic criterion to identify these queries and prove its sufficiency. We also prove the strong result that every group query has an equivalent formulation that satisfies our syntactic criterion. We describe a general evaluation technique for group queries, and demonstrate how an optimizer can determine this plan. We then consider more complex queries whose components are group queries with potentially different partitioning attributes. We give two methods to identify group query components within such a query. We also give some performance results for group queries expressed in standard SQL, comparing a commercial database system with our optimized plan on top of the same commercial system. These results indicate that there are significant potential performance improvements.
38852147
On Negation in HiLog
Abstract The logic HiLog of Chen, Kifer, and Warren has a second order syntax, while its semantics is first order. HiLog programs with negative literals in the body are considered. A stable-model semantics and a well-founded semantics for this class of program are defined, and it is shown that these semantics generalize the stable-model semantics and the well-founded semantics, respectively, for range-restricted normal programs. A second order property called preservation under extensions is proposed and investigated. Preservation under extensions ensures that the semantics of a program is not changed when rules having no symbols in common with the program are appended to the program. It is shown that for normal programs, domain independence and preservation under extensions are equivalent, while for HiLog programs, preservation under extensions is strictly stronger. Range restrictedness is generalized to HiLog programs in two ways, and it is shown that range restricted HiLog programs are preserved under extensions with respect to the well-founded semantics. Conditions under which the well-founded semantics is two-valued are investigated, and the class of modularly stratified programs is generalized to HiLog. An extension of magic-set techniques to modularly stratified HiLog programs is described.
31185043
Inferring negative information from disjunctive databases
We propose criteria that any rule for inferring negative information from disjunctive databases should satisfy, and examine existing rules from this viewpoint. We then present a new inference rule, the ‘disjunctive database rule’ (DDR), and compare it to the existing rules with respect to the criteria. In particular, the DDR is equivalent to the CWA for definite databases, it infers no more negative information than the GCWA, and it interprets disjunction inclusively rather than exclusively. We generalize the DDR to a class of layered databases, describe an implementation of the DDR, ‘negation as positive failure’, and study its soundness and completeness properties.
11677427
Stochastic fluid models for cache clusters
Clusters of Web caches are extensively used by different types of organizations, including companies, universities, ISPs, and CDNs. To model Web caches, we must account for two types of stochastic events: objects being pulled into/out of the cache cluster at random times, and caches going up and down at random times. Detailed stochastic models of such complex systems quickly become intractable. In this paper we propose a stochastic fluid model which captures the salient characteristics of a cache cluster. The stochastic fluid model replaces the object arrivals to the cluster and departures (object modification/expiration) with a fluid flow, but maintains the up/down dynamics of the original system. The model can be applied to a variety of cluster routing policies, and provides a simple means to estimate the hit rate. We compare the results of the stochastic fluid model with that of a simulation of the real system. We find the fluid model to not only be a close approximation, but also to exhibit the key qualitative properties of the original system. We conclude that stochastic fluid models show great potential in modeling a variety of content distribution systems.
15587034
Packet Scheduling Across Networks of Switches
Recent developments in computer and communication networks require scheduling decisions to be made under increasingly complex system dynamics. We model and analyze the problem of packet transmissions through an arbitrary network of buffered queues, and provide a framework for describing routing and migration. This paper introduces an intuitive geometric description of stability for these networks and describes some simple algorithms which lead to maximal throughput. We show how coordination over sequential timeslots by algorithms such as those based on a round robin can provide considerable advantages over a randomized scheme.
8733679
Stochastic Fluid Theory for P2P Streaming Systems
We develop a simple stochastic fluid model that seeks to expose the fundamental characteristics and limitations of P2P streaming systems. This model accounts for many of the essential features of a P2P streaming system, including the peers' realtime demand for content, peer churn (peers joining and leaving), peers with heterogeneous upload capacity, limited infrastructure capacity, and peer buffering and playback delay. The model is tractable, providing closed-form expressions which can be used to shed insight on the fundamental behavior of P2P streaming systems. The model shows that performance is largely determined by a critical value. When the system is of moderate-to-large size, if a certain ratio of traffic loads exceeds the critical value, the system performs well; otherwise, the system performs poorly. Furthermore, large systems have better performance than small systems since they are more resilient to bandwidth fluctuations caused by peer churn. Finally, buffering can dramatically improve performance in the critical region, for both small and large systems. In particular, buffering can bring more improvement than can additional infrastructure bandwidth.
1775458
Optimal streaming of layered video
This paper presents a model and theory for streaming layered video. We model the bandwidth available to the streaming application as a stochastic process whose statistical characteristics are unknown a priori. The random bandwidth models short-term variations due to congestion control (such as TCP-friendly conformance). We suppose that the video has been encoded into a base and an enhancement layer, and that to decode the enhancement layer the base layer has to be available to the client. We make the natural assumption that the client has abundant local storage and attempts to prefetch as much of the video as possible during playback. At any instant of time, starvation or partial starvation can occur at the client in either of the two layers. During periods of starvation, the client applies video error concealment to hide the loss. We study the dynamic allocation of the available bandwidth to the two layers in order to minimize the impact pact of client starvation. For the case of an infinitely-long video, we find that the optimal policy takes on a surprisingly simple and static form. For finite-length videos, the optimal policy is a simple static policy when the enhancement layer is deemed at least as important as the base layer. When the base layer is more important, we design a threshold policy heuristic which switches between two static policies. We provide numerical results that compare the performance of no-prefetching, static and threshold policies.
5328792
Interactive video streaming with proxy servers
We study caching strategies for proxies that cache VBR-encoded continuous media objects for highly interactive streaming applications. First, we develop a model for streaming VBR-encoded continuous media objects. This model forms the basis for a stream admission control criterion and our study of caching strategies. We find that unlike conventional web caches, proxy caches for continuous media objects need to replicate or stripe objects to achieve high hit rates. We develop novel caching strategies that either implicitly or explicitly track the request pattern and cache (and replicate) objects accordingly. Our numerical results indicate that our caching strategies achieve significantly higher hit rates than caching without object replication.