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49
Small Byzantine Quorum Systems
 DISTRIBUTED COMPUTING
, 2001
"... In this paper we present two protocols for asynchronous Byzantine Quorum Systems (BQS) built on top of reliable channelsone for selfverifying data and the other for any data. Our protocols tolerate Byzantine failures with fewer servers than existing solutions by eliminating nonessential work in ..."
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Cited by 404 (49 self)
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In this paper we present two protocols for asynchronous Byzantine Quorum Systems (BQS) built on top of reliable channelsone for selfverifying data and the other for any data. Our protocols tolerate Byzantine failures with fewer servers than existing solutions by eliminating nonessential work in the write protocol and by using read and write quorums of different sizes. Since engineering a reliable network layer on an unreliable network is difficult, two other possibilities must be explored. The first is to strengthen the model by allowing synchronous networks that use timeouts to identify failed links or machines. We consider running synchronous and asynchronous Byzantine Quorum protocols over synchronous networks and conclude that, surprisingly, "selftiming" asynchronous Byzantine protocols may offer significant advantages for many synchronous networks when network timeouts are long. We show how to extend an existing Byzantine Quorum protocol to eliminate its dependency on reliable networking and to handle message loss and retransmission explicitly.
Identifying the minimal transversals of a hypergraph and related problems
 SIAM Journal on Computing
, 1995
"... The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertic ..."
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Cited by 126 (7 self)
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The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be coNPcomplete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs, is shown to be computationally equivalent to transversal hypergraph recognition, i.e., given two hypergraphs H 1; H 2, decide if the sets in H 2 are all the minimal transversals of H 1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size, but it is unknown whether an outputpolynomial algorithm exists for this problem. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, we present outputpolynomial algorithms. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and AI, particularly in modelbased diagnosis.
The Load, Capacity and Availability of Quorum Systems
, 1998
"... A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is th ..."
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Cited by 89 (12 self)
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A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is the minimal access probability of the busiest element, minimizing over the strategies. The capacity Cap(S) is the highest quorum accesses rate that S can handle, so Cap(S) = 1=L(S).
Computational Complexity of Terminological Reasoning in BACK
 Artificial Intelligence
, 1988
"... Terminological reasoning is a mode of reasoning all hybrid knowledge representation systems based on KLONE rely on. After a short introduction of what terminological reasoning amounts to, it is proven that a complete inference algorithm for the BACK system would be computationally intractable. Inte ..."
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Cited by 61 (11 self)
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Terminological reasoning is a mode of reasoning all hybrid knowledge representation systems based on KLONE rely on. After a short introduction of what terminological reasoning amounts to, it is proven that a complete inference algorithm for the BACK system would be computationally intractable. Interestingly, this result also applies to the KANDOR system, which had been conjectured to realize complete terminological inferences with a tractable algorithm. More generally, together with an earlier paper of Brachman and Levesque it shows that terminological reasoning is intractable for any system using a nontrivial description language. Finally, consequences of this distressing result are briefly discussed. 1 Introduction The BACK system 1 [13] belongs to the class of hybrid knowledge representation systems based on KLONE (cf. the article by Brachman and Schmolze [4]). As in any other system of this family, a framebased description language (henceforth FDL), which can be viewed as a ...
Cluster Graph Modification Problems
 Discrete Applied Mathematics
, 2002
"... In a clustering problem one has to partition a set of elements into homogeneous and wellseparated subsets. From a graph theoretic point of view, a cluster graph is a vertexdisjoint union of cliques. The clustering problem is the task of making fewest changes to the edge set of an input graph so th ..."
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Cited by 60 (5 self)
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In a clustering problem one has to partition a set of elements into homogeneous and wellseparated subsets. From a graph theoretic point of view, a cluster graph is a vertexdisjoint union of cliques. The clustering problem is the task of making fewest changes to the edge set of an input graph so that it becomes a cluster graph. We study the complexity of three variants of the problem. In the Cluster Completion variant edges can only be added. In Cluster Deletion, edges can only be deleted. In Cluster Editing, both edge additions and edge deletions are allowed. We also study these variants when the desired solution must contain a prespecified number of clusters.
Access control and signatures via quorum secret sharing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1998
"... We suggest a method of controlling the access to a secure database via quorum systems. A quorum system is a collection of sets (quorums) every two of which have a nonempty intersection. Quorum systems have been used for a number of applications in the area of distributed systems. We propose a separ ..."
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Cited by 34 (13 self)
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We suggest a method of controlling the access to a secure database via quorum systems. A quorum system is a collection of sets (quorums) every two of which have a nonempty intersection. Quorum systems have been used for a number of applications in the area of distributed systems. We propose a separation between access servers, which are protected and trustworthy, but may be outdated, and the data servers, which may all be compromised. The main paradigm is that only the servers in a complete quorum can collectively grant (or revoke) access permission. The method we suggest ensures that, after authorization is revoked, a cheating user Alice will not be able to access the data even if many access servers still consider her authorized and even if the complete raw database is available to her. The method has a low overhead in terms of communication and computation. It can also be converted into a distributed system for issuing secure signatures. An important building block in our method is the use of secret sharing schemes that realize the access structures of quorum systems. We provide several efficient constructions of such schemes which may be of interest in their own right.
Are Quorums an Alternative for Data Replication
 ACM TRANSACTIONS ON DATABASE SYSTEMS
, 2003
"... ... this article, we analyze several quorum types in order to better understand their behavior in practice. The results obtained challenge many of the assumptions behind quorum based replication. Our evaluation indicates that the conventional readone/writeallavailable approach is the best choice ..."
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Cited by 33 (10 self)
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... this article, we analyze several quorum types in order to better understand their behavior in practice. The results obtained challenge many of the assumptions behind quorum based replication. Our evaluation indicates that the conventional readone/writeallavailable approach is the best choice for a large range of applications requiring data replication. We believe this is an important result for anybody developing code for computing clusters as the readone/writeallavailable strategy is much simpler to implement and more flexible than quorumbased approaches. In this article, we show that, in addition, it is also the best choice using a number of other selection criteria
Improved bounds and algorithms for hypergraph twocoloring
, 1998
"... We show that for all large n, every nuniform hypergraph with at most 0:7pn = ln n \Theta 2n edges can be 2colored. This makes progress on a problem of Erd""os (1963), improving the previousbest bound of n1=3 \Gamma o(1) \Theta 2n due to Beck (1978). We further generalize this to a ..."
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Cited by 32 (0 self)
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We show that for all large n, every nuniform hypergraph with at most 0:7pn = ln n \Theta 2n edges can be 2colored. This makes progress on a problem of Erd""os (1963), improving the previousbest bound of n1=3 \Gamma o(1) \Theta 2n due to Beck (1978). We further generalize this to a
Crumbling Walls: A Class of Practical and Efficient Quorum Systems
, 1996
"... A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information In this paper we introduce a general class of quorum ..."
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Cited by 32 (8 self)
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A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information In this paper we introduce a general class of quorum systems called Crumbling Walls and study its properties. The elements (processors) of a wall are logically arranged in rows of varying widths. A quorum in a wall is the union of one full row and a representative from every row below the full row. This class considerably generalizes a number of known quorum system constructions. The best crumbling wall is the CWlog quorum system. It has small quorums, of size O(lg n), and structural simplicity. The CWlog has optimal availability and optimal load among systems with such small quorum size. It manifests its high quality for all universe sizes, so it is a good choice not only for systems with thousands or millions of processors but also for systems with as few as 3 or 5 processors. Moreover, our analysis shows that the availability will increase and the load will decrease at the optimal rates as the system increases in size.
Hardness of approximate hypergraph coloring
 SICOMP: SIAM Journal on Computing
"... We introduce the notion of covering complexity of a verifier for probabilistically checkable proofs (PCP). Such a verifier is given an input, a claimed theorem, and an oracle, representing a purported proof of the theorem. The verifier is also given a random string and decides whether to accept the ..."
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Cited by 31 (3 self)
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We introduce the notion of covering complexity of a verifier for probabilistically checkable proofs (PCP). Such a verifier is given an input, a claimed theorem, and an oracle, representing a purported proof of the theorem. The verifier is also given a random string and decides whether to accept the proof or not, based on the given random string. We define the covering complexity of such a verifier, on a given input, to be the minimum number of proofs needed to “satisfy ” the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to getting stronger inapproximability results for some minimization problems, and in particular, (hyper)graph coloring problems. We present a PCP verifier for NP statements that queries only four bits and yet has a covering complexity of one for true statements and a superconstant covering complexity for statements not in the language. Moreover, the acceptance predicate of this verifier is a simple NotallEqual check on the four bits it reads. This enables us to prove that for any constant c, it is NPhard to color a 2colorable 4uniform hypergraph using just c colors, and also yields a superconstant inapproximability result under a stronger hardness