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The Nature of Statistical Learning Theory
, 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
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Cited by 13236 (32 self)
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Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based
New approximation algorithms for the TSP
"... The traveling salesman problem (TSP) is probably the best known combinatorial optimization problem. Although studied intensively for sixty years, the TSP continues to pose grand challenges. Cook’s [2012] recent book gives an excellent introduction. Since the TSP is NPhard (Karp [1972]), it is natu ..."
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]), it is natural to ask for approximation algorithms. How good solutions can we guarantee to find in polynomial time? Christofides [1976] devised a 3 2approximation algorithm for the Symmetric TSP: it always finds a solution that is at most 50 % longer than optimum. Can we do better? Can we do similarly well
New approximation algorithms for graph coloring
 J. ACM
, 1994
"... The problem of coloring a graph with the minimum number of colors is well known to be NPhard, even restricted to kcolorable graphs for constant k ≥ 3. This paper explores the approximation problem of coloring kcolorable graphs with as few additional colors as possible in polynomial time, with spe ..."
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Cited by 46 (3 self)
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The problem of coloring a graph with the minimum number of colors is well known to be NPhard, even restricted to kcolorable graphs for constant k ≥ 3. This paper explores the approximation problem of coloring kcolorable graphs with as few additional colors as possible in polynomial time
New Approximation Algorithms for the Steiner Tree Problems
"... The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solution ..."
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Cited by 51 (5 self)
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The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal
New approximation algorithms for minimum cycle bases of graphs
 In STACS 2007, 24th Annual Symposium on Theoretical Aspects of Computer Science, volume 4393 of LNCS
, 2007
"... We consider the problem of computing an approximate minimum cycle basis of an undirected nonnegative edgeweighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space ov ..."
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Cited by 4 (2 self)
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can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k ≥ 1, we give (2k−1
New Approximation Algorithms for Minimum Enclosing Convex Shapes
"... Given n points in a d dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all n points. We give two approximation algorithms for producing an enclosing ball whose radius is at most ɛ away from the optimum. The first requir ..."
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Cited by 3 (0 self)
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Given n points in a d dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all n points. We give two approximation algorithms for producing an enclosing ball whose radius is at most ɛ away from the optimum. The first
New Approximation Algorithms for Vehicle Scheduling Problems
"... We consider makespan minimization for vehicle scheduling problems on trees with release and handling times. 2approximation algorithms were known for several variants of the single vehicle problem on a path [15]. A 3=2approximation algorithm was known for the single vehicle problem on a path whe ..."
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We consider makespan minimization for vehicle scheduling problems on trees with release and handling times. 2approximation algorithms were known for several variants of the single vehicle problem on a path [15]. A 3=2approximation algorithm was known for the single vehicle problem on a path
New Approximation Algorithm for Minimum Steiner Tree Problem
"... The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices which are called required. If the edge weights are all positive, then the resulting subgraph is obviously a tree. The computational nature of the problem makes ..."
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makes it a traditional research subject in theory of computing. Steiner tree problem in graphs is NPcomplete, i.e., the exact optimal solutions are unlikely computable in polynomialtime unless P=NP. We present a new polynomial time approximation algorithm
New Approximation Algorithms for Routing with MultiPort Terminals
"... Previous literature on VLSI routing and wiring estimation typically assumes a onetoone correspondence between terminals and ports. In practice, however, each "terminal" consists of a large collection of electrically equivalent ports, a fact that is not accounted for in layout steps such ..."
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Cited by 1 (1 self)
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such as wiring estimation. In this paper, we address the general problem of minimumcost routing tree construction in the presence of multiport terminals, which gives rise to the group Steiner minimal tree problem. Our main result is the first known approximation algorithm for the group Steiner problem with a
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