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4,117
Worst case bounds for shortest path interval routing
, 1995
"... Consider shortest path interval routing, a popular memory-balanced method for solving the routing problem on arbitrary networks. Given a network G, let Irs(G) denote the maximum number of intervals necessary to encode groups of destinations on an edge, minimized over all shortest path interval routi ..."
Abstract
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Cited by 25 (12 self)
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routing schemes on G. In this paper, we establish tight worst case bounds on Irs(G). More precisely for any n, we construct a network G of n nodes with Irs(G) 2 (n), thereby improving on the best known lower bound of (n = log n). We also establish a worst case bound on bounded degree networks: for any 3
Worst-Case Bounds for Subadditive Geometric Graphs
- Proc. 9th ACM Symp. Comp. Geom
, 1993
"... We consider graphs such as the minimum spanning tree, minimum Steiner tree, minimum matching, and traveling salesman tour for n points in the d-dimensional unit cube. For each of these graphs, we show that the worst-case sum of the dth powers of edge lengths is O(log n). This is a consequence of ..."
Abstract
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Cited by 13 (1 self)
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) for minimum matching, but #(log n) for traveling salesman tour, which answers a question of Snyder and Steele. 1. Introduction A worst-case, or a priori , bound on a geometric graph is a bound that depends only on the assumption that all vertices lie within a given container. Such a bound does not depend
Worst-case Bounds for the Logarithmic Loss of Predictors
, 1999
"... We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of ..."
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Cited by 11 (1 self)
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of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric
WORST CASE BOUNDS FOR THE EUCLIDEAN MATCHING PROBLEM
, 1981
"... It is shown how the classical mathematical theory of sphere packing can be used to obtain bounds for a greedy heuristic for the bounded euclidean matching problem. In the case of 2 dimensions, bounds are obtained directly. For higher dimensions, an appeal is made to known bounds for the sphere pack ..."
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Cited by 2 (0 self)
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It is shown how the classical mathematical theory of sphere packing can be used to obtain bounds for a greedy heuristic for the bounded euclidean matching problem. In the case of 2 dimensions, bounds are obtained directly. For higher dimensions, an appeal is made to known bounds for the sphere
Worst case bounds in the presence of correlated uncertainty
, 2006
"... This paper presents a method for computing rigorous bounds on the solution of linear systems whose coefficients have large, correlated uncertainties, with a computable overestimation factor that is frequently quite small. Linear systems of equations are among the most frequently used tools in applie ..."
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case results are needed. For example, current safety regulation laws in civil engineering require a worst case analysis, and hence interval techniques, although current practice is still Monte Carlo with its deficiencies. Recently, NEUMAIER & POWNUK ( 2) showed that using interval analysis
On domain-partitioning induction criteria: worst-case bounds for the worst-case based
, 2004
"... ..."
A Worst-case Bound for Topology Computation of Algebraic Curves
- J. Symb. Comput
"... Computing the topology of an algebraic plane curve C means to compute a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with coefficients bounded by 2ρ, the topology of the induced curve can be computed with Õ(n8(n+ρ2)) b ..."
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Cited by 10 (5 self)
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Computing the topology of an algebraic plane curve C means to compute a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with coefficients bounded by 2ρ, the topology of the induced curve can be computed with Õ(n8(n+ρ2
A GENERIC WORST-CASE BOUND ON THE CONDITION NUMBER OF A HOMOTOPY PATH
"... Abstract. The number of steps of homotopy algorithms for solving systems of polynomials is usually bounded by the condition number of the homotopy path. A generic bound on the condition number of homotopy path between systems with integer coefficients will be given. 1. ..."
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Abstract. The number of steps of homotopy algorithms for solving systems of polynomials is usually bounded by the condition number of the homotopy path. A generic bound on the condition number of homotopy path between systems with integer coefficients will be given. 1.
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