Results 1  10
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96
Hamiltonian Triangulations for Fast Rendering
, 1994
"... Highperformance rendering engines in computer graphics are often pipelined, and their speed is bounded by the rate at which triangulation data can be sent into the machine. To reduce the data rate, it is desirable to order the triangles so that consecutive triangles share a face, meaning that only ..."
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Cited by 73 (9 self)
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Highperformance rendering engines in computer graphics are often pipelined, and their speed is bounded by the rate at which triangulation data can be sent into the machine. To reduce the data rate, it is desirable to order the triangles so that consecutive triangles share a face, meaning that only one additional vertex need be transmitted to describe each triangle. Such an ordering exists if and only if the dual graph of the triangulation contains a Hamiltonian path. In this paper, we consider several problems concerning triangulations with Hamiltonian duals. Specifically, we ffl Show that any set of n points in the plane has a Hamiltonian triangulation, and give two optimal \Theta(n log n) algorithms for constructing such a triangulation. We have implemented and tested both algorithms. ffl Consider the special case of sequential triangulations, where the Hamiltonian cycle is implied, and prove that certain nondegenerate point sets in the plane do not admit a sequential triangulati...
The median problems for breakpoints are NPcomplete
 Elec. Colloq. on Comput. Complexity
, 1998
"... The breakpoint distance between two npermutations is the number of pairs that appear consecutively in one but not in the other. In the median problem for breakpoints one is given a set of permutations and has to construct a permutation that minimizes the sum of breakpoint distances to all the origi ..."
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Cited by 71 (1 self)
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The breakpoint distance between two npermutations is the number of pairs that appear consecutively in one but not in the other. In the median problem for breakpoints one is given a set of permutations and has to construct a permutation that minimizes the sum of breakpoint distances to all the original ones. Recently, the problem was suggested as a model for determining the evolutionary history of several species based on their gene orders. We show that the problem is already NPhard for three permutations, and that this result holds both for signed and for unsigned permutations.
Four Strikes against Physical Mapping of DNA
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 1993
"... Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete ..."
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Cited by 68 (8 self)
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Physical Mapping is a central problem in molecular biology ... and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NPcomplete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the kconsecutive ones problem for k >= 2. These models have been chosen to reflect various features typical in biological data, including false negative and positive errors, small width of the map and chimericism.
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 68 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
Hardness and approximation results for black hole search in arbitrary graphs
 In Proc. 12th Coll. on Structural Information and Communication complexity (SIROCCO’05
, 2005
"... Abstract. A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous arbitrary network, assuming an upper bound on the ti ..."
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Cited by 30 (11 self)
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Abstract. A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous arbitrary network, assuming an upper bound on the time of any edge traversal by an agent. For a given graph and a given starting node we are interested in finding the fastest possible Black Hole Search by two agents (the minimum number of agents capable to identify a black hole). We prove that this problem is NPhard in arbitrary graphs, thus solving an open problem stated in [2]. We also give a 7/2approximation algorithm, thus improving on the 4approximation scheme observed in [2]. Our approach is to explore the given input graph via some spanning tree. Even if it represents a very natural technique, we prove that this approach cannot achieve an approximation ratio better than 3/2.
Computing Simple Circuits from a Set of Line Segments . . .
, 1987
"... Given a collection of line segments in the plane we would like to connect the segments by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon.) However, there are collections of line segments where this cannot be done. In this note it is proved that d ..."
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Cited by 26 (1 self)
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Given a collection of line segments in the plane we would like to connect the segments by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon.) However, there are collections of line segments where this cannot be done. In this note it is proved that deciding whether a set of line segments admits a simple circuit is NPcomplete. Deciding whether a set of horizontal line segments can be connected with horizontal and vertical line segments to construct an orthogonal simple circuit is also shown to be NPcomplete.
Flowshop scheduling with limited temporary storage
 Journal of the ACM
, 1980
"... We examine the problem of scheduling 2machine flowshops in order to minimize makespan, using a limited amount of intermediate storage buffers. Although there are efficient algorithms for the extreme cases of zero and infinite buffer capacities, we show that all the intermediate (finite capacity) ca ..."
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Cited by 26 (0 self)
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We examine the problem of scheduling 2machine flowshops in order to minimize makespan, using a limited amount of intermediate storage buffers. Although there are efficient algorithms for the extreme cases of zero and infinite buffer capacities, we show that all the intermediate (finite capacity) cases are NPcomplete. We prove exact bounds for the relative improvement of execution times when a given buffer capacity is used. We also analyze an efficient heuristic for solving the 1buffer problem, showing that it has a 3/2 worstcase performance. Furthermore, we show that the &quot;nowait &quot; (i.e., zero buffer) flowshop scheduling problem with 4 machines is NPcomplete. This partly settles a wellknown open question, although the 3machine case is left open here. *Research supported by NSF Grant MCS7701192 +Research supported by NSF/RANN grant APR7612036
Computing phylogenetic roots with bounded degrees and errors
 SIAM Journal on Computing
, 2003
"... Given a set of species and their similarity data, an important problem in evolutionary biology is how to reconstruct a phylogeny (also called evolutionary tree) so that species are close in the phylogeny if and only if they have high similarity. Assume that the similarity data are represented as a g ..."
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Cited by 21 (1 self)
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Given a set of species and their similarity data, an important problem in evolutionary biology is how to reconstruct a phylogeny (also called evolutionary tree) so that species are close in the phylogeny if and only if they have high similarity. Assume that the similarity data are represented as a graph G = (V, E) where each vertex represents a species and two vertices are adjacent if they represent species of high similarity. The phylogeny reconstruction problem can then be abstracted as the problem of finding a (phylogenetic) tree T from the given graph G such that (1) T has no degree2 internal nodes, (2) the external nodes (i.e. leaves) of T are exactly the elements of V, and (3) (u, v) ∈ E if and only if dT (u, v) ≤ k for some fixed threshold k, where dT (u, v) denotes the distance between u and v in tree T. This is called the Phylogenetic kth Root Problem (PRk), and such a tree T, if exists, is called a phylogenetic kth root of graph G. The computational complexity of PRk is open, except for k ≤ 4. In this paper, we investigate PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant. Our main contribution is a lineartime algorithm that determines if G has such a phylogenetic kth root, and if so, demonstrates one. On the other hand, as in practice the collected similarity data are usually not perfect and may contain errors, we propose to study a generalized version of PRk where the output phylogeny is only required to be an approximate root of the input graph. We show that this and other related problems are computationally intractable. Keywords: Phylogeny, phylogenetic root, computational biology, efficient algorithm, NPhard. 1
Alpha Coverage: Bounding the Interconnection Gap for Vehicular Internet Access
, 2009
"... Abstract—Vehicular Internet access via open WLAN access points (APs) has been demonstrated to be a feasible solution to provide opportunistic data service to moving vehicles. Using an in situ deployment, however, such a solution does not provide worstcase performance guarantees due to unpredictable ..."
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Cited by 19 (4 self)
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Abstract—Vehicular Internet access via open WLAN access points (APs) has been demonstrated to be a feasible solution to provide opportunistic data service to moving vehicles. Using an in situ deployment, however, such a solution does not provide worstcase performance guarantees due to unpredictable intermittent connectivity. On the other hand, a solution that tries to cover every point in an entire road network with APs (full coverage) is not very practical due to the prohibitive deployment and operational cost. In this paper, we introduce a new notion of intermittent coverage for mobile users, called αcoverage, which provides worstcase guarantees on the interconnection gap while using significantly fewer APs than needed for full coverage. We propose efficient algorithms to verify whether a given deployment provides αcoverage and approximation algorithms for determining a deployment of APs that will provide αcoverage. We compare αcoverage with opportunistic access of open WLAN APs (modeled as a random deployment) via simulations over a realworld road network and show that using the same number of APs as random deployment, αcoverage bounds the interconnection gap to a much smaller distance than that in a random deployment. I.