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A New Tight Upper Bound on the Transposition Distance
 PROCEEDINGS OF THE FIFTH WORKSHOP ON ALGORITHMS IN BIOINFORMATICS (WABI)
, 2005
"... We study the problem of computing the minimal number of adjacent, nonintersecting block interchanges required to transform a permutation into the identity permutation. In particular, we use the graph of a permutation to compute that number for a particular class of permutations in linear time and s ..."
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Cited by 5 (1 self)
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and space, and derive a new tight upper bound on the socalled transposition distance.
A Tight Upper Bound on the Number of Candidate Patterns
, 2001
"... In the context of mining for frequent patterns using the standard levelwise algorithm, the following question arises: given the current level and the current set of frequent patterns, what is the maximal number of candidate patterns that can be generated on the next level? We answer this question by ..."
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Cited by 8 (1 self)
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by providing a tight upper bound, derived from a combinatorial result from the sixties by Kruskal and Katona. Our result is useful to reduce the number of database scans.
Tight upper bounds for Streett and parity complementation
 In Proc
"... Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic, modelchecking, program analysis and verification. For Streett complementation, a significant gap ..."
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Cited by 6 (2 self)
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complementation construction with upper bound 2O(n lgn+nk lg k) for k = O(n) and 2O(n2 lgn) for k = ω(n), which matches well the lower bound obtained in [3]. We also obtain a tight upper bound 2O(n lgn) for parity complementation.
Tight Upper Bound on Useful Distributed System Checkpoints
 Coordinated Science Laboratory, University of Illinois at UrbanaChampaign
, 1995
"... In this paper, we give an alternative proof of the necessary and sufficient condition for achieving optimal checkpoint garbage collection in distributed systems [9]. We show that, by formulating the recovery line calculation problem as a reachability analysis problem on a rollbackdependency graph, ..."
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Cited by 3 (1 self)
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In this paper, we give an alternative proof of the necessary and sufficient condition for achieving optimal checkpoint garbage collection in distributed systems [9]. We show that, by formulating the recovery line calculation problem as a reachability analysis problem on a rollbackdependency graph, the proof can be greatly simplified. We also present a polynomialtime optimal garbage collection algorithm based on a graph search. Keywords: fault tolerance, distributed systems 1 Introduction A checkpoint is a snapshot of process state, saved on nonvolatile storage to survive failures. A process periodically takes checkpoints during its execution so that when its volatile state is lost due to a failure, the execution can resume from a checkpointed state (an action called rollback recovery) instead of from the very beginning. In a distributed system, two checkpoints c 1 and c 2 of two processes p 1 and p 2 are inconsistent if a message was sent from p 1 after c 1 and received by p 2 bef...
Tight Upper Bound on Useful Distributed System Checkpoints
 Coordinated Science Laboratory, University of Illinois at UrbanaChampaign
, 2001
"... In this paper, we give an alternative proof of the necessary and sufficient condition for achieving optimal checkpoint garbage collection in distributed systems [9]. We show that, by formulating the recovery line calculation problem as a reachability analysis problem on a rollbackdependency graph, ..."
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In this paper, we give an alternative proof of the necessary and sufficient condition for achieving optimal checkpoint garbage collection in distributed systems [9]. We show that, by formulating the recovery line calculation problem as a reachability analysis problem on a rollbackdependency graph, the proof can be greatly simplified. We also present a polynomialtime optimal garbage collection algorithm based on a graph search.
A Tight Upper Bound on the Cover Time for Random Walks on Graphs
, 1995
"... We prove that the expected time for a random walk to visit all n vertices of a connected graph is at most 4 27 n 3 + o(n 3 ). 1 Introduction Let G = G(V; E) be a simple connected undirected graph with n vertices and m edges. We consider simple random walks on G, where at each step the rand ..."
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Cited by 59 (7 self)
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We prove that the expected time for a random walk to visit all n vertices of a connected graph is at most 4 27 n 3 + o(n 3 ). 1 Introduction Let G = G(V; E) be a simple connected undirected graph with n vertices and m edges. We consider simple random walks on G, where at each step the random walk moves to a vertex chosen at random with uniform probability from the neighbors of the current vertex. Let u and v denote two vertices. The hitting time H[u; v] is the expected number of steps it takes a walk that starts at u to reach v. The commute time C[u; v] is the expected number of steps that it takes a walk to go from u to v and back to u (that is, C[u; v] = H[u; v] +H[v;u]). The cover time EC[v] is the expected number of steps it takes a random walk that starts at v to visit all vertices of the graph. For a graph G(V; E) its hitting time H[G] (commute time C[G], cover time EC[G], respectively) is defined as H[G] = max u;v2V [H[u; v]] (C[G] = max u;v2V [C[u; v]] , EC[G] = max v...
Almost tight upper bounds for vertical decompositions in four dimensions
 In Proc. 42nd IEEE Symposium on Foundations of Computer Science
, 2001
"... We show that the complexity of the vertical decomposition of an arrangement of n fixeddegree algebraic surfaces or surface patches in four dimensions is O(n 4+ε), for any ε> 0. This improves the best previously known upper bound for this problem by a nearlinear factor, and settles a major proble ..."
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Cited by 32 (5 self)
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We show that the complexity of the vertical decomposition of an arrangement of n fixeddegree algebraic surfaces or surface patches in four dimensions is O(n 4+ε), for any ε> 0. This improves the best previously known upper bound for this problem by a nearlinear factor, and settles a major
Almost tight upper bounds for the single cell and zone problems in three dimensions
 Geom
, 1995
"... We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n lowdegree algebraic surface patches in 3space. We show that this complexity is O(n ..."
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Cited by 33 (18 self)
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We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n lowdegree algebraic surface patches in 3space. We show that this complexity is O(n
Results 1  10
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