8247434
NP-Hard Sets are Superterse Unless NP is Small
Abstract We show that the class P- mc ( n ) of polynomial time n -membership comparable sets (defined by Ogihara, 1995) has p -measure 0. Using this result, we will show that the class of sets which are ⩽ tt P -reducible to some P-selective set has p -measure 0. Furthermore, we will show that if NP does not have p -measure 0 then no ⩽ tt p -hard set for NP is P-approximable.
5135938
Privacy preserving database application testing
Traditionally, application software developers carry out their tests on their own local development databases. However, such local databases usually have only a small number of sample data and hence cannot simulate satisfactorily a live environment, especially in terms of performance and scalability testing. On the other hand, the idea of testing applications over live production databases is increasingly problematic in most situations primarily due to the fact that such use of live production databases has the potential to expose sensitive data to an unauthorized tester and to incorrectly update information in the underlying database. In this paper, we investigate techniques to generate mock databases for application software testing without revealing any confidential information from the live production databases. Specifically, we will design mechanisms to create the deterministic rule set R, non-deterministic rule set N R, and statistic data set S for a live production database. We will then build a security Analyzer which will process the triplet <R',N R',S'> together with security requirements (security policy) and output a new triplet <R',N R',S'> The security Analyzer will guarantee that no confidential information could be inferred from the new triplet <R',N R',S'> The mock database generated from this new triplet can simulate the live environment for testing purpose, while maintaining the privacy of data in the original database.
6216289
Efficient and Secure Storage Systems Based on Peer-to-Peer Systems
Two fundamental problems that confront peer-to-peer applications are to efficiently locate the node that stores a data object and to achieve data security (e.g., confidentiality, integrity, authentication, and authorization). This paper presents a model for secure distributed applications based on peer-to-peer systems and presents Chord , a distributed lookup protocol that address the data object location problem in peer-to-peer systems. The protocol Chord is a novel combination of Chord and Tapestry/Plaxton-Rajaraman-Richa with provable better performance. In particular, node insertion in our scheme could be finished in steps (all other existing node insertion algorithms for peer-to-peer systems take steps—see the summary in Hildrum et al.).
8968053
Resource-Bounded Balanced Genericity, Stochasticity and Weak Randomness
We introduce balanced t(n)-genericity which is a refinement of the genericity concept of Ambos-Spies, Fleischhack and Huwig [2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity [6]. By uniformly describing these concepts and weaker notions of stochasticity introduced by Wilber [19] and Ko [11] in terms of prediction functions, we clarify the relations among these resource-bounded stochasticity concepts. Moreover, we give descriptions of these concepts in the framework of Lutz's resource-bounded measure theory [13] based on martingales: We show that t(n)-stochasticity coincides with a weak notion of t(n)-randomness based on so-called simple martingales but that it is strictly weaker than t(n)-randomness in the sense of Lutz.
41292415
Randomness, Stochasticity and Approximations
Polynomial time unsafe approximations for intractable sets were introduced by Meyer and Paterson [9] and Yesha [19], respectively. The question of which sets have optimal unsafe approximations has been investigated extensively; see, e.g., [1], [5], [15], and [17]. Recently, Wang [15], [17] showed that polynomial time random sets are neither optimally unsafe approximable nor Δ -levelable. In this paper we show that: (1) There exists a polynomial time stochastic set in the exponential time complexity class which has an optimal unsafe approximation. (2) There exists a polynomial time stochastic set in the exponential time complexity class which is Δ -levelable. The above two results answer a question asked by Ambos-Spies and Lutz [2]: What kind of natural complexity property can be characterized by p -randomness but not by p -stochasticity? Our above results also extend Ville's [13] historical result. The proof of our first result shows that, for Ville's stochastic sequence, we can find an optimal prediction function f such that we will never lose our own money betting according to f (except the money we have earned), that is to say, if at the beginning we have only $1 and we always bet $1 that the next selected bit is 1 , then we always have enough money to bet on the next bit. Our second result shows that there is a stochastic sequence for which there is a betting strategy f such that we will never lose our own money betting according to f (except the money we have earned), but there is no such optimal betting strategy. That is to say, for any such betting strategy, we can find another betting strategy which could be used to make money more quickly.
18269009
Maximum Flows and Critical Vertices in AND/OR Graphs
We will study this problem and present an algorithm for finding the minimum-time-cost solution graph in an AND/OR graph. We will also study the following problems which often appear in industry when using AND/OR graphs to model manufacturing processes or to model problem solving processes: finding maximum (additive and nonadditive) flows and critical vertices in an AND/OR graph. Though there are well known polynomial time algorithms for the corresponding problems in the traditional graph theory, we will show that generally it is NP-hard to find a non-additive maximum flow in an AND/OR graph, and it is both NP-hard and coNP-hard to find a set of critical vertices in an AND/OR graph. We will also present a polynomial time algorithm for finding a maximum additive flow in an AND/OR graph, and discuss the relative complexity of these problems.
34251654
Near-Linear Time Approximation Algorithms for Curve Simplification
We consider the problem of approximating a polygonal curve P under a given error criterion by another polygonal curve P? whose vertices are a subset of the vertices of P. The goal is to minimize the number of vertices of P? while ensuring that the error between P? and P is below a certain threshold. We consider two fundamentally different error measures -- Hausdorff and Frechet error measures. For both error criteria, we present near-linear time approximation algorithms that, given a parameter ? > 0, compute a simplified polygonal curve P? whose error is less than ? and size at most the size of an optimal simplified polygonal curve with error ?/2. We consider monotone curves in the case of Hausdorff error measure and arbitrary curves for the Frechet error measure. We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice.
1622745
Replication-based efficient data delivery scheme (red) for delay/fault-tolerant mobile sensor network (DFT-MSN)
The delay/fault-tolerant mobile sensor network (DFT-MSN) has been proposed recently for pervasive information gathering. DFT-MSN distinguishes itself from conventional sensor networks by several unique characteristics such as sensor mobility, loose connectivity, and delay/fault tolerability. The mainstream approaches for sensor networking/communication cannot be applied in DFT-MSN directly. In this paper we propose a replication-based efficient data delivery (RED) scheme based on erasure coding technology tailored for DFT-MSN. RED consists of two key components for data transmission and message management, respectively. The former makes decision on when and where to transmit data messages according to the delivery probability. The latter decides the optimal erasure coding parameters (including the number of data blocks and the needed redundancy) based on its current delivery probability, in order to achieve the desired data delivery ratio while minimizing overhead at the same time. Extensive simulation has been carried out for performance evaluation. Compared with other approaches, the proposed RED data delivery scheme achieves high message delivery ratio with low transmission overhead and data management complexity
2472095
Coarse and Reliable Geometric Alignment for Protein Docking
We present an efficient algorithm for generating a small set of coarse alignments between interacting proteins using meaningful features on their surfaces. The proteins are treated as rigid bodies, but the results are more generally useful as the produced configurations can serve as input to local improvement algorithms that allow for protein flexibility. We apply our algorithm to a diverse set of protein complexes from the Protein Data Bank, demonstrating the effectivity of our algorithm, both for bound and for unbound protein docking problems.
16315333
Computing feedback laws for linear systems with a parallel pieri homotopy
Homotopy methods to solve polynomial systems are well suited for parallel computing because the solution paths defined by the homotopy can be tracked independently. Both the static and dynamic load balancing models are implemented in C with MPI, adapting PHCpack written in Ada using gcc, and tested on academic benchmarks and mechanical applications. We studied the parallelization of Pieri homotopies to compute all feedback laws to control linear systems. To distribute the workload, we mapped the poset onto a tree. As the dimensions of the Pieri homotopies grow incrementally from the root to the leaves in the tree, we found the Pieri homotopies well suited for parallel computing.
13312657
Feedback vertex sets in star graphs
In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for star graphs. Also by applying the properties of regular graphs, a lower bound can easily be achieved for star graphs.