Polynomial Worst-case Time Research Articles

One step at a time: An efficient approach to query-based ontology debugging

When ontologies reach a certain size and complexity, faults such as inconsistencies, unsatisfiable classes or wrong entailments are hardly avoidable. Locating the incorrect axioms that cause these faults is a hard and time-consuming task. Addressing this issue, several techniques for a semi-automatic fault localization in ontologies have been proposed and extensively studied. One class of these approaches involve a human expert who provides answers to system-generated queries about the intended (correct) ontology in order to reduce the possible fault locations. To suggest as informative questions as possible, existing methods draw on various algorithmic optimizations as well as heuristics. However, these computations are often based on certain assumptions about the interacting expert.In this work, we demonstrate that these assumptions might not always be adequate and discuss consequences of their violations. In particular, we characterize a range of expert types with different query answering behavior and show that existing approaches are far from achieving optimal efficiency for all of them. In addition, we find that the cost metric adopted by state-of-the-art techniques might not always be realistic and that a change of metric has a decisive impact on the best choice of query answering strategy. As a remedy, we suggest a new – and simpler – type of expert question that leads to a stable fault localization performance for all analyzed expert types and effort metrics, and has numerous further advantages over existing techniques. Moreover, we present an algorithm which computes and optimizes this new query type in worst-case polynomial time and which is fully compatible with existing concepts (e.g., query selection heuristics) and infrastructure (e.g., debugging user interfaces) in the field.Comprehensive experiments on faulty real-world ontologies attest that the new querying method is substantially and statistically significantly superior to existing techniques both in terms of the number of necessary expert interactions and in terms of the query computation time. We find that relying on the new querying method can save an interacting expert more than 80% of their work, and can reduce the expert’s waiting time for the next query by more than three orders of magnitude. Beside these findings, we demonstrate that the efficiency of existing query-based tools can be significantly boosted by suggesting an appropriate query answering strategy to an expert; we also make recommendations in this regard. Further, we suggest optimal configurations of a debugger for situations where the new type of query is used.Remarkably, the proposed approach is not only applicable to ontologies, but to any monotonic knowledge representation language, and can even be adopted to solve general model-based diagnosis problems expressible using Reiter’s theory.

Cooperative Spectrum Sensing as Image Segmentation: A New Data Fusion Scheme

Reliable and efficient identification of spectrum access opportunities is crucial for cognitive radio ad hoc networks (CRAHNs). A promising method to improve sensing reliability is CSS, where sensing data from multiple secondary users is combined to facilitate decision making. However, the performance of CSS algorithms in CRAHNs is limited by two challenges. First, the spectrum occupancy status in CRAHNs is spatially heterogeneous. Second, malfunctioning nodes or malicious attackers may falsify the true sensing results. To handle both these challenges, inspired by image segmentation in computer vision, we propose a novel graph-cut CSS algorithm. This algorithm is robust in the presence of false sensing data reports, computationally efficient (with polynomial worst case time complexity), and can be implemented distributively. Theoretically, it can be regarded as a new data fusion scheme that is generalized from classical likelihood ratio tests when sensing information is fully exploited, or from the majority fusion rule, when thresholded sensing information is utilized. Introduction

Low-Complexity Optimal Hard Decision Fusion Under the Neyman–Pearson Criterion

The design of the optimal nonrandomized hard decision fusion rule under the Neyman–Pearson criterion is known to be exponential in complexity. In this letter, we formulate a more generalized version of this problem called the “generalized decision fusion problem (GDFP)” and relate it to the classical $\text{0--1}$ knapsack problem. Consequently, we show that the GDFP has a worst-case polynomial time solution. Numerical results are presented to verify the effectiveness of the proposed solution.

Computation with multiple CTCs of fixed length and width

We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of the classes of languages decided by polynomial time probabilistic and quantum computers that can send a single classical bit to their own past. We show that, given a time machine with constant negative delay, one can implement CTC-based computations without the need to know about the runtime beforehand. Chaining multiple instances of such fixed-length CTCs, the power of postselection can be endowed to deterministic computers, all languages in $$\mathsf{NP} \cup \mathsf{coNP}$$ can be decided with no error in worst-case polynomial time, and all Turing-decidable languages can be decided in constant expected time. We provide proofs of the following facts for weaker models: Augmenting probabilistic computers with a single CTC leads to an improvement in language recognition power. Quantum computers under these restrictions are more powerful than their classical counterparts. Some deterministic models assisted with multiple CTCs are more powerful than those with a single CTC.

Design of Multiunit Electronic Exchanges Through Decomposition

In this paper, we exploit the idea of decomposition to match buyers and sellers in an electronic exchange for trading large volumes of homogeneous goods, where the buyers and sellers specify marginal-decreasing piecewise constant price curves to capture volume discounts. Such exchanges are relevant for automated trading in many e-business applications. The problem of determining winners and Vickrey prices in such exchanges is known to have a worst-case complexity equal to that of as many as (1+m+n) NP-hard problems, where m is the number of buyers and n is the number of sellers. Our method proposes the overall exchange problem to be solved as two separate and simpler problems: 1) forward auction and 2) reverse auction, which turns out to be generalized knapsack problems. In the proposed approach, we first determine the quantity of units to be traded between the sellers and the buyers using fast heuristics developed by us. Next, we solve a forward auction and a reverse auction using fully polynomial time approximation schemes available in the literature. The proposed approach has worst-case polynomial time complexity and our experimentation shows that the approach produces good quality solutions to the problem. Note to Practitioners- In recent times, electronic marketplaces have provided an efficient way for businesses and consumers to trade goods and services. The use of innovative mechanisms and algorithms has made it possible to improve the efficiency of electronic marketplaces by enabling optimization of revenues for the marketplace and of utilities for the buyers and sellers. In this paper, we look at single-item, multiunit electronic exchanges. These are electronic marketplaces where buyers submit bids and sellers ask for multiple units of a single item. We allow buyers and sellers to specify volume discounts using suitable functions. Such exchanges are relevant for high-volume business-to-business trading of standard products, such as silicon wafers, very large-scale integrated chips, desktops, telecommunications equipment, commoditized goods, etc. The problem of determining winners and prices in such exchanges is known to involve solving many NP-hard problems. Our paper exploits the familiar idea of decomposition, uses certain algorithms from the literature, and develops two fast heuristics to solve the problem in a near optimal way in worst-case polynomial time

On Testing a Bivariate Polynomial for Analytic Reducibility

LetKbe an algebraically closed field of characteristic zero. We present an efficient algorithm for determining whether or not a given polynomialf(x,y) inK[x,y] is analytically reducible overKat the origin. The algorithm presented is based upon an informal method sketched by Kuo (1989) which is in turn derived from ideas of Abhyankar (1988). The presentation contained herein emphasises the proofs of the algorithm's correctness and termination, and is suitable for computer implementation. A polynomial worst case time complexity bound is proved for a partial version of the algorithm.

Determining optimal binary inter-relational clustering schema for a relational database*

Clustering the related tuples of a pair of relations that are in many-to-one relationship (We call it inter-clustering.) expedites equijoin and natural join operations on these base relations. However, inter-clustering slows down other relational algebra operations. Thus it is important to determine globally the pairs of relations to inter-cluster. In this paper we present a methodology which first finds out the candidate pairs of relations to inter-cluster from database accesses. Then it determines an optimal schema consisting of pairs of relations to inter-cluster, using a global optimization algorithm based on a weighted graph matching solution. The objective of the optimization is minimizing the cost of processing the relational algebra operations on the base relations associated with the database accesses. The optimization algorithm gives an exact solution and is not a heuristic one. The whole methodology is of polynomial worst case time order complexity. The proof of correctness of the various steps...

Oracle Quantum Computing

Abstract Building on the work of Deutsch and Jozsa, we construct oracles relative to which (1) there is a decision problem that can be solved with certainty in worst-case polynomial time on the quantum computer, yet it cannot be solved classically in probabilistic expected polynomial time if errors are not tolerated, nor even in nondeterministic polynomial time, and (2) there is a decision problem that can be solved in exponential time on the quantum computer, which requires double exponential time on all but finitely many instances on any classical deterministic computer.

Polynomial-average-time satisfiability problems

A class of random conjunctive-normal-form (CNF) predicates is characterized by v, the number of variables from which literals may be formed (giving 2 v literals); p( v), the probability that a given literal is in a random clause; and t( v), the number of random independently selected clauses in a random predicate. Determining satisfiability on such a class using backtracking takes polynomial average time under the following conditions: (1) lim v → ∞ vp( v) = 0 and t(v) ⩾ ( ln2 + ϵ)v [− ln((v + l)p(v))] ; and (2) lim vp( v) = ∞, lim p( v) = 0, and t(v) ⩾ [ ( ln2 + ϵ) ep(v) ] exp [2vp(v)] for any fixed ϵ > 0. Additional cases are also covered. An analysis by Goldberg showed that problems for which p( v) is constant can be solved in polynomial average time by a simplified Davis-Putnam procedure. We give an algorithm for solving problems with t(v) ⩽ ( ln lnv) ln3 in polynomial worst-case time. Thus all problem sets for which p( v) or t( v) grows extremely rapidly or extremely slowly can be solved in polynomial average time. We also show that backtracking requires exponential average time when lim vp( v) = 0 and t(v) ⩽ ( ln2 − ϵ)v [− ln((v + 1)p(v))] , and when lim vp( v) = ∞, lim v → ∞ vp( v) = 0, and t(v) ⩽ [ ( ln2 − ge) ep(v) ] exp[2vp(v)] .