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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.
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 5 (1 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.
A tight upper bound on acquaintance time of graphs
, 2014
"... In this note we confirm a conjecture raised by Benjamini et al. [BST13] on the acquaintance time of graphs, proving that for all graphs G with n vertices it holds that AC(G) = O(n3/2), which is tight up to a multiplicative constant. This is done by proving that for all graphs G with n vertices and ..."
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Cited by 4 (1 self)
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and maximal degree ∆ it holds that AC(G) ≤ 20∆n. Combining this with the bound AC(G) ≤ O(n2/∆) from [BST13] gives the foregoing uniform upper bound of all nvertex graphs. We also prove that for the nvertex path Pn it holds that AC(Pn) = n − 2. In addition we show that the barbell graph Bn consisting
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 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 31 (17 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
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