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Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
Abstract

Cited by 357 (6 self)
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In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied
Notes On The Topological Tverberg Theorem
, 1998
"... . Following a manuscript of K. S. Sarkaria we give an extensive account of the topological Tverberg Theorem in the case where the number of desired disjoint faces is a prime power. Since all known proofs of the theorem use methods from algebraic topology, the objective of this paper is to explain th ..."
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Cited by 12 (0 self)
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. Following a manuscript of K. S. Sarkaria we give an extensive account of the topological Tverberg Theorem in the case where the number of desired disjoint faces is a prime power. Since all known proofs of the theorem use methods from algebraic topology, the objective of this paper is to explain
Tverberg’s theorem with constraints
 J. Combinatorial Theory, Ser. A
, 2008
"... The topological Tverberg theorem claims that for any continuous map of the (q − 1)(d + 1)simplex σ (d+1)(q−1) to R d there are q disjoint faces of σ (d+1)(q−1) such that their images have a nonempty intersection. This has been proved for affine maps, and if q is a prime power, but not in general. ..."
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Cited by 7 (1 self)
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The topological Tverberg theorem claims that for any continuous map of the (q − 1)(d + 1)simplex σ (d+1)(q−1) to R d there are q disjoint faces of σ (d+1)(q−1) such that their images have a nonempty intersection. This has been proved for affine maps, and if q is a prime power, but not in general
Tverberg graphs
, 2008
"... The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)simplex to R d, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the sa ..."
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The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)simplex to R d, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed
On the Topological Tverberg Theorem
, 2008
"... Helge Tverberg proved in 1966 that for every linear map from the ((d + 1)(q − 1))dimensional simplex ∆ (d+1)(q−1) into R d there is a set of q disjoint faces of this simplex such that their images intersect in a point [Tve66]. It is conjectured that such a set of disjoint faces exists for every con ..."
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Cited by 1 (1 self)
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continuous map ∆ (d+1)(q−1) → R d as well, but no complete proof of such a “Topological Tverberg Theorem ” is known yet. Up to now, it has only been proven that the conjecture holds in the case that q is a prime power [Vol96]. A proof of the Topological Tverberg Theorem for arbitrary q is considered as one
ON A THEOREM OF TVERBERG
"... Let ∆ n denote the ndimensional simplex. Any face of ∆ n is assumed to be closed. The wellknown theorem of Radon (see [6]) can be formulated as follows Theorem (Radon). For any linear map f: ∆n+1 → Rn there exist two disjoint faces σ1, σ2 of ∆n+1 such that f(σ1) ∩ f(σ2) = ∅. ..."
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Let ∆ n denote the ndimensional simplex. Any face of ∆ n is assumed to be closed. The wellknown theorem of Radon (see [6]) can be formulated as follows Theorem (Radon). For any linear map f: ∆n+1 → Rn there exist two disjoint faces σ1, σ2 of ∆n+1 such that f(σ1) ∩ f(σ2) = ∅.
Tverbergtype theorems . . .
"... Let S be a ddimensional separoid of (k − 1)(d + 1) + 1 convex sets in some ‘largedimensional ’ Euclidean space IE N. We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a ddimensional separoid of points P in general position, then there ex ..."
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Let S be a ddimensional separoid of (k − 1)(d + 1) + 1 convex sets in some ‘largedimensional ’ Euclidean space IE N. We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a ddimensional separoid of points P in general position
Tverberg partitions and Borsuk–Ulam theorems
 Pacific Jour. of Math
"... An Ndimensional real representation E of a finite group G is said to have the “Borsuk–Ulam Property ” if any continuous Gmap from the (N + 1)fold join of G (an Ncomplex equipped with the diagonal Gaction) to E has a zero. This happens iff the “Van Kampen characteristic class ” of E is nonzero, ..."
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Cited by 13 (0 self)
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, so using standard computations one can explicitly characterize representations having the BU property. As an application we obtain the “continuous ” Tverberg theorem for all prime powers q, i.e., that some q disjoint faces of a (q − 1)(d+ 1)dimensional simplex must intersect under any continuous
Scaling theorems for zero crossings
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... We prove that the scale map of the zerocrossings of atmost all signals filtered by the second derivative of a gaussian of variable size determines the signal uniquely, up to a constant scaling and a harmonic function. Our proof provides a method for reconstructing almost all signals from knowledge ..."
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Cited by 181 (4 self)
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. Stability of the reconstruction scheme is briefly discussed. The result applies to zero and levelcrossings of linear differential operators of gaussian filters. The theorem is extended to two dimensions, that is to images. These results are reminiscent of Logan's theorem. They imply that extrema
The Topological Tverberg Theorem and winding numbers
 JOURNAL OF COMBINATORIAL THEORY, SERIES A
, 2005
"... The Topological Tverberg Theorem claims that any continuous map of a (q − 1)(d + 1)simplex to R d identifies points from q disjoint faces. (This has been proved for affine maps, for d ≤ 1, and if q is a prime power, but not yet in general.) The Topological Tverberg Theorem can be restricted to maps ..."
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Cited by 4 (0 self)
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The Topological Tverberg Theorem claims that any continuous map of a (q − 1)(d + 1)simplex to R d identifies points from q disjoint faces. (This has been proved for affine maps, for d ≤ 1, and if q is a prime power, but not yet in general.) The Topological Tverberg Theorem can be restricted to maps
Results 1  10
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1,347