pinecone/core-2020-05-10-deduplication huggingface dataset:
An Improved Approximation Algorithm for MULTIWAY CUT

AbstractGiven an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due to Dahlhaus, Johnson, Papadimitriou, Seymour, and Yannakakis gave a performance guarantee of 2(1−1k). In this paper, we present a new linear programming relaxation for Multiway Cut and a new approximation algorithm based on it. The algorithm breaks the threshold of 2 for approximating Multiway Cut, achieving a performance ratio of at most 1.5−1k. This improves the previous result for every value of k. In particular, for k=3 we get a ratio of 76<43
On Indexed Data Broadcast

AbstractWe consider the problem of efficient information retrieval in asymmetric communication environments where multiple clients with limited resources retrieve information from a powerful server who periodically broadcasts its information repository over a communication medium. The cost of a retrieving client consists of two components: (a) access time, defined as the total amount of time spent by a client in retrieving the information of interest, and (b) tuning time, defined as the time spent by the client in actively listening to the communication medium, measuring a certain efficiency in resource usage. A probability distribution is associated with the data items in the broadcast, representing the likelihood of a data item's being requested at any point of time. The problem of indexed data broadcast is to schedule the data items interleaved with certain indexing information in the broadcast so as to minimize simultaneously the mean access time and the mean tuning time. Prior work on this problem thus far has focused only on some special cases. In this paper we study the indexed data broadcast problem in its full generality and design a broadcast scheme that achieves a mean access time of at most (1.5+ε) times the optimal and a mean tuning time bounded by O(logn)
Protecting Data Privacy in Private Information Retrieval Schemes

AbstractPrivate information retrieval (PIR) schemes allow a user to retrieve the ith bit of an n-bit data string x, replicated in k⩾2 databases (in the information-theoretic setting) or in k⩾1 databases (in the computational setting), while keeping the value of i private. The main cost measure for such a scheme is its communication complexity. In this paper we introduce a model of symmetrically-private information retrieval (SPIR), where the privacy of the data, as well as the privacy of the user, is guaranteed. That is, in every invocation of a SPIR protocol, the user learns only a single physical bit of x and no other information about the data. Previously known PIR schemes severely fail to meet this goal. We show how to transform PIR schemes into SPIR schemes (with information-theoretic privacy), paying a constant factor in communication complexity. To this end, we introduce and utilize a new cryptographic primitive, called conditional disclosure of secrets, which we believe may be a useful building block for the design of other cryptographic protocols. In particular, we get a k-database SPIR scheme of complexity O(n1/(2k−1)) for every constant k⩾2 and an O(logn)-database SPIR scheme of complexity O(log2n·loglogn). All our schemes require only a single round of interaction, and are resilient to any dishonest behavior of the user. These results also yield the first implementation of a distributed version of (n1)-OT (1-out-of-n oblivious transfer) with information-theoretic security and sublinear communication complexity
Min-Wise Independent Permutations

AbstractWe define and study the notion of min-wise independent families of permutations. We say that F⊆Sn (the symmetric group) is min-wise independent if for any set X⊆[n] and any x∈X, when π is chosen at random in F we havePr(min{π(X)}=π(x))=1|X| . In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under π. Our research was motivated by the fact that such a family (under some relaxations) is essential to the algorithm used in practice by the AltaVista web index software to detect and filter near-duplicate documents. However, in the course of our investigation we have discovered interesting and challenging theoretical questions related to this concept—we present the solutions to some of them and we list the rest as open problems
The Closure of Monadic NP

AbstractIt is a well-known result of Fagin that the complexity class NP coincides with the class of problems expressible in existential second-order logic (Σ11), which allows sentences consisting of a string of existential second-order quantifiers followed by a first-order formula. Monadic NP is the class of problems expressible in monadic Σ11, i.e., Σ11 with the restriction that the second-order quantifiers are all unary and hence range only over sets (as opposed to ranging over, say, binary relations). For example, the property of a graph being 3-colorable belongs to monadic NP, because 3-colorability can be expressed by saying that there exists three sets of vertices such that each vertex is in exactly one of the sets and no two vertices in the same set are connected by an edge. Unfortunately, monadic NP is not a robust class, in that it is not closed under first-order quantification. We define closed monadic NP to be the closure of monadic NP under first-order quantification and existential unary second-order quantification. Thus, closed monadic NP differs from monadic NP in that we allow the possibility of arbitrary interleavings of first-order quantifiers among the existential unary second-order quantifiers. We show that closed monadic NP is a natural, rich, and robust subclass of NP. As evidence for its richness, we show that not only is it a proper extension of monadic NP, but that it contains properties not in various other extensions of monadic NP. In particular, we show that closed monadic NP contains an undirected graph property not in the closure of monadic NP under first-order quantification and Boolean operations. Our lower-bound proofs require a number of new game-theoretic techniques
Computing with Membranes

AbstractWe introduce a new computability model, of a distributed parallel type, based on the notion of a membrane structure. Such a structure consists of several cell-like membranes, recurrently placed inside a unique “skin” membrane. A plane representation is a Venn diagram without intersected sets and with a unique superset. In the regions delimited by the membranes there are placed objects. These objects are assumed to evolve: each object can be transformed in other objects, can pass through a membrane, or can dissolve the membrane in which it is placed. A priority relation between evolution rules can be considered. The evolution is done in parallel for all objects able to evolve. In this way, we obtain a computing device (we call it a P system): start with a certain number of objects in a certain membrane and let the system evolve; if it will halt (no object can further evolve), then the computation is finished, with the result given as the number of objects in a specified membrane. If the development of the system goes forever, then the computation fails to have an output. We prove that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice. In fact, we do not need cooperating rules, but we only use catalysts, specified objects which are present in the rules but are not modified by the rule application. One catalyst suffices. A variant is also considered, with the objects being strings over a given alphabet. The evolution rules are now based on string transformations. We investigate the case when either the rewriting operation from Chomsky grammars (with respect to context-free productions) or the splicing operation from H systems investigated in the DNA computing is used. In both cases, characterizations of recursively enumerable languages are obtained by very simple P systems: with three membranes in the rewriting case and four in the splicing case. Several open problems and directions for further research are formulate
The Security of the Cipher Block Chaining Message Authentication Code

AbstractLet F be some block cipher (eg., DES) with block length l. The cipher block chaining message authentication code (CBC MAC) specifies that an m-block message x=x1…xm be authenticated among parties who share a secret key a for the block cipher by tagging x with a prefix of ym, where y0=0l and yi=Fa(mi⊕yi−1) for i=1, 2, …, m. This method is a pervasively used international and U.S. standard. We provide its first formal justification, showing the following general lemma: cipher block chaining a pseudorandom function yields a pseudorandom function. Underlying our results is a technical lemma of independent interest, bounding the success probability of a computationally unbounded adversary in distinguishing between a random ml-bit to l-bit function and the CBC MAC of a random l-bit to l-bit function
Improved Algorithms via Approximations of Probability Distributions

AbstractWe present two techniques for constructing sample spaces that approximate probability distributions. The first is a simple method for constructing the small-bias probability spaces introduced by Naor and Naor. We show how to efficiently combine this construction with the method of conditional probabilities to yield improved parallel algorithms for problems such as set discrepancy, finding large cuts in graphs, and finding large acyclic subgraphs. The second is a construction of small probability spaces approximating general independent distributions which are of smaller size than the constructions of Even, Goldreich, Luby, Nisan, and Veličković
Semantics and Expressive Power of Nondeterministic Constructs in Deductive Databases

AbstractNondeterministic extensions are needed in logic-based languages, such as first-order relational languages and Datalog, to enhance their expressive power and support the efficient formulation of low-complexity problems and database queries. In this paper, we study the semantics and expressive power of the various nondeterministic constructs proposed in the past, including various versions of the choice operator and the witness operator. The paper develops a model-theoretic semantics, a fixpoint semantics, and an operational semantics for these constructs, and characterizes their power of expressing deterministic and nondeterministic queries. The paper presents various soundness and completeness results and establishes an expressiveness hierarchy that correlates the various operators with each other and with other constructs such as negation and fixpoint
Belief Revision and Update: Complexity of Model Checking

AbstractOne of the main challenges in the formal modeling of common-sense reasoning is the ability to cope with the dynamic nature of the world. Among the approaches put forward to address this problem are belief revision and update. Given a knowledge base T, representing our knowledge of the “state of affairs” of the world of interest, it is possible that we are led to trust another piece of information P, possibly inconsistent with the old one T. The aim of revision and update operators is to characterize the revised knowledge base T′ that incorporates the new formula P into the old one T while preserving consistency and, at the same time, avoiding the loss of too much information. In this paper we study the computational complexity, in the propositional case, of one of the main reasoning problems of belief revision and update: deciding if an interpretation M is a model of the revised knowledge base
Robust Learning Is Rich

AbstractIntuitively, a class of objects is robustly learnable if not only this class itself is learnable but all of its computable transformations remain learnable as well. In that sense, being learnable robustly seems to be a desirable property in all fields of learning. We will study this phenomenon within the paradigm of inductive inference. Here a class of recursive functions is called robustly learnable under the criterion I iff all of its images under general recursive operators are learnable under the criterion I. M. Fulk (1990, in “3lst Annual IEEE Symposium on Foundations of Computer Science,” pp. 405–410, IEEE Comput. Soc. Press, Los Alamitos, CA) showed the existence of a nontrivial class which is robustly learnable under the criterion Ex. However, several of the hierarchies (such as the anomaly hierarchies for Ex and Bc) do not stand robustly. Hence, up to now it was not clear if robust learning is really rich. The main intention of this paper is to give strong evidence that robust learning is rich. Our main result proved by a priority construction is that the mind change hierarchy for Ex stands robustly. Moreover, the hierarchies of team learning for both Ex and Bc stand robustly as well. In several contexts, we observe the surprising fact that a more complex topological structure of the classes to be learned leads to positive robustness results, whereas an easy topological structure yields negative results. We also show the counterintuitive fact that even some self-referential classes can be learned robustly. Some of our results point out the difficulty of robust learning when only a bounded number of mind changes is allowed. Further results concerning uniformly robust learning are derived
On the Benefit of Supporting Virtual Channels in Wormhole Routers

AbstractThis paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in O((L+D)C(DlogD)1/B/B) flit steps, where a flit step is the time taken to transmit B flits, i.e., one flit per virtual channel, across a physical channel. We also prove a nearly matching lower bound; i.e., for any values of C, D, B, and L, where C, D⩾B+1 and L=(1+Ω(1))D, we show how to construct a network and a set of L-flit messages whose paths have congestion C and dilation D that require Ω(LCD1/B/B) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor significantly larger than B. We also present a simple randomized wormhole routing algorithm for the butterfly network. The algorithm routes any q-relation on the inputs and outputs of an n-input butterfly in O(L(q+logn)log1/Bnloglog(qn)/B) flit steps. We present a nearly-matching lower bound that holds for a broad class of algorithms
Inductive Inference with Additional Information

AbstractWe consider the problem of inductively inferring a grammar for a language, given (positive) examples of the language and putative (possibly faulty) grammars for the complement of the language. The criterion of success is identification in the limit, defined by E. M. Gold (1967, Inform. and Control10, 447–474). Additional information is useful insofar as it allows the identification of language classes that would not be identified with positive examples alone. An infinite sequence of grammars past some finite position are correct for the complement of the input language, is not as useful a form of additional information as a single correct grammar for the complement. Grammars that are almost correct for the complement (that is, that make finitely many errors) are not as useful as correct grammars, and the usefulness of a grammar decreases with increasing numbers of errors
Full Intersection Types and Topologies in Lambda Calculus

AbstractTopologies are introduced on the set of lambda terms by their typeability in the full intersection type assignment system. These topologies give rise to simple proofs of some fundamental results of the lambda calculus such as the continuity theorem and the genericity lemma. We show that application is continuous, unsolvable terms are bottoms, and normal forms are isolated points with respect to these topologies. The restriction of all these topologies to the set of closed lambda terms appears to be unique. We compare the introduced topology with the filter topology on the set of (closed) lambda terms and show that they coincide
A Fault-Tolerance Model for Multiprocessor Real-Time Systems

AbstractSystem reliability is an important aspect of real-time systems, because the result of a real-time application may be valid only if the application functions correctly and its timing constraints are satisfied. There are two kinds of faults, hardware and software faults, and the paper considers hardware transient faults. Full replication or full hardware redundancy can achieve a high degree of reliability; however, it wastes lots of resources. For most real-time systems, such schemes might not be available and hence reliability estimation becomes essential. We propose an analytic model for system reliability estimation based on the Markov chain and investigate the accuracy of the estimated reliability. The results show that the proposed model obtains good estimation in various simulated real-time systems
Relational Transducers for Electronic Commerce

AbstractElectronic commerce is emerging as one of the major Web-supported applications requiring database support. We introduce and study high-level declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational transducers that map sequences of input relations into sequences of output relations. The semantically meaningful trace of an input–output exchange is kept as a sequence of log relations. We consider problems motivated by electronic commerce applications, such as log validation, verifying temporal properties of transducers, and comparing two relational transducers. Positive results are obtained for a restricted class of relational transducers called Spocus transducers (for semi-positive outputs and cumulative state). We argue that despite the restrictions, these capture a wide range of practically significant business models
Efficient Searching with Linear Constraints

AbstractWe show how to preprocess a set S of points in Rd into an external memory data structure that efficiently supports linear-constraint queries. Each query is in the form of a linear constraint xd⩽a0+∑d−1i=1aixi; the data structure must report all the points of S that satisfy the constraint. This problem is called halfspace range searching in the computational geometry literature. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d=2, we present the first data structure that uses linear space and answers linear-constraint queries using an optimal number of I/Os in the worst case. For d=3, we present a near-linear-size data structure that answers queries using an optimal number of I/Os on the average. We present linear-size data structures that can answer d-dimensional linear-constraint queries (and even more general d-dimensional simplex queries) efficiently in the worst case. For the d=3 case, we also show how to obtain trade-offs between space and query time
Path Constraints in Semistructured Databases

AbstractWe investigate a class of path constraints that is of interest in connection with both semistructured and structured data. In standard database systems, constraints are typically expressed as part of the schema, but in semistructured data there is no explicit schema and path constraints provide a natural alternative. As with structured data, path constraints on semistructured data express integrity constraints associated with the semantics of data and are important in query optimization. We show that in semistructured databases, despite the simple syntax of the constraints, their associated implication problem is r.e. complete and finite implication problem is co-r.e. complete. However, we establish the decidability of the implication and finite implication problems for several fragments of the path constraint language and demonstrate that these fragments suffice to express important semantic information such as extent constraints, inverse relationships, and local database constraints commonly found in object-oriented databases
Latent Semantic Indexing: A Probabilistic Analysis

AbstractLatent semantic indexing (LSI) is an information retrieval technique based on the spectral analysis of the term-document matrix, whose empirical success had heretofore been without rigorous prediction and explanation. We prove that, under certain conditions, LSI does succeed in capturing the underlying semantics of the corpus and achieves improved retrieval performance. We propose the technique of random projection as a way of speeding up LSI. We complement our theorems with encouraging experimental results. We also argue that our results may be viewed in a more general framework, as a theoretical basis for the use of spectral methods in a wider class of applications such as collaborative filtering
Querying Spatial Databases via Topological Invariants

AbstractThe paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered are first-order on the spatial database side, and fixpoint+counting, fixpoint, and first-order on the topological invariant side. In particular, it is shown that fixpoint+counting expresses precisely all the ptime queries on topological invariants; if the regions are connected, fixpoint expresses all ptime queries on topological invariants