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Making Nondeterminism Unambiguous
, 1997
"... We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly Lo ..."
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Cited by 36 (10 self)
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We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to contextfree languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly LogCFL/poly = UAuxPDA(log n; n O(1) )/poly
The Complexity of Planarity Testing
, 2000
"... We clarify the computational complexity of planarity testing, by showing that planarity testing is hard for L, and lies in SL. This nearly settles the question, since it is widely conjectured that L = SL [25]. The upper bound of SL matches the lower bound of L in the context of (nonuniform) circ ..."
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Cited by 23 (7 self)
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We clarify the computational complexity of planarity testing, by showing that planarity testing is hard for L, and lies in SL. This nearly settles the question, since it is widely conjectured that L = SL [25]. The upper bound of SL matches the lower bound of L in the context of (nonuniform) circuit complexity, since L/poly is equal to SL/poly. Similarly, we show that a planar embedding, when one exists, can be found in FL SL . Previously, these problems were known to reside in the complexity class AC 1 , via a O(log n) time CRCW PRAM algorithm [22], although planarity checking for degreethree graphs had been shown to be in SL [23, 20].
SIGACT News Complexity Theory Column 19
, 1997
"... this paper describes the complete problems that motivate interest in these classes, discusses some surprising recent discoveries, and points out open problems where progress can reasonably be expected. 3 Definitions ..."
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this paper describes the complete problems that motivate interest in these classes, discusses some surprising recent discoveries, and points out open problems where progress can reasonably be expected. 3 Definitions
SIGACT News Complexity Theory Column 19
"... this paper describes the complete problems that motivate interest in these classes, discusses some surprising recent discoveries, and points out open problems where progress can reasonably be expected ..."
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this paper describes the complete problems that motivate interest in these classes, discusses some surprising recent discoveries, and points out open problems where progress can reasonably be expected
RUSPACE(log n) \subseteq DSPACE(log² n/log log n)
 THE 7TH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION (ISAAC’96
, 1998
"... We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine. ..."
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We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# timebounded algorithm for this problem running on a parallel pointer machine.
Parallelized approximation algorithms for minimum routing cost spanning trees
, 705
"... Let G = (V, E) be an undirected graph with a nonnegative edgeweight function w. The routing cost of a spanning tree T of G is ∑ u,v∈V dT (u, v), where dT (u, v) denotes the weight of the simple uv path in T. The Minimum Routing Cost Spanning Tree (MRCT) problem [WLB+ 00] asks for a spanning tree o ..."
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Let G = (V, E) be an undirected graph with a nonnegative edgeweight function w. The routing cost of a spanning tree T of G is ∑ u,v∈V dT (u, v), where dT (u, v) denotes the weight of the simple uv path in T. The Minimum Routing Cost Spanning Tree (MRCT) problem [WLB+ 00] asks for a spanning tree of G with the minimum routing cost. In this paper, we parallelize several previously proposed approximation algorithms for the MRCT problem and some of its variants. Let ɛ> 0 be an arbitrary constant. When the edgeweight function w is given in unary, we parallelize the (4/3 + ɛ)approximation algorithm for the MRCT problem [WCT00b] by implementing it using an RN C circuit. There are other variants of the MRCT problem. In the SumRequirement Optimal Communication Spanning Tree (SROCT) problem [WCT00a], each vertex u is associated with a requirement r(u) ≥ 0. The objective is to find a spanning tree T of G minimizing ∑ u,v∈V (r(u) + r(v)) dT (u, v). When the edgeweight function w and the vertexrequirement function r are given in unary, we parallelize the 2approximation algorithm for the SROCT problem [WCT00a] by realizing it using RN C circuits, with a slight degradation in the approximation ratio from 2 to 2 + o(1). In the weighted 2MRCT problem [Wu02], we have additional inputs s1, s2 ∈ V and λ ≥ 1. The objective is to find a spanning tree T of G minimizing ∑ v∈V λ dT (s1, v) + dT (s2, v). When the edgeweight function w is given in unary, we parallelize the 2approximation algorithm [Wu02] into RN C circuits, with a slight degradation in the approximation ratio from 2 to 2 + o(1). To the best of our knowledge, our results are the first parallelized approximation algorithms for the MRCT problem and its variants. 1