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On the Minimum Number of

by unknown authors
"... A family P = {π1,..., πq} of permutations of [n] = {1,..., n} is completely k-scrambling [Spencer, 1972; Füredi, 1996] if for any distinct k points x1,..., xk ∈ [n], permutations πi’s in P produce all k! possible orders on πi(x1),..., πi(xk). Let N ∗ (n, k) be the minimum size of such a family. Thi ..."
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A family P = {π1,..., πq} of permutations of [n] = {1,..., n} is completely k-scrambling [Spencer, 1972; Füredi, 1996] if for any distinct k points x1,..., xk ∈ [n], permutations πi’s in P produce all k! possible orders on πi(x1),..., πi(xk). Let N ∗ (n, k) be the minimum size of such a family

The Minimum Number of Monotone Subsequences

by Joseph Samuel Myers , 2002
"... Erdos and Szekeres showed that any permutation of length n +1contains a monotone subsequence of length k + 1. A simple example shows that there need be no more than (n mod k) such subsequences; we conjecture that this is the minimum number of such subsequences. We prove this fo ..."
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Erdos and Szekeres showed that any permutation of length n +1contains a monotone subsequence of length k + 1. A simple example shows that there need be no more than (n mod k) such subsequences; we conjecture that this is the minimum number of such subsequences. We prove

The Minimum Number of Hubs in Networks

by Easton Li, Xu Guangyue Han
"... In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size or the ..."
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In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size

ROUTING WITH MINIMUM NUMBER OF LANDMARKS

by Jun Luo, Rong Peng, Chenglin Fan, Jinxing Hu
"... Routing problem has been studied for decades. In this paper, we focus on one of the routing problems: finding a path from source to destination on road network with the guidance of landmarks. People use landmarks to identify previously visited places and reoriented themselves in the environment. Whe ..."
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at least one landmark to be seen at any point along the way. Therefore, the problem becomes: find a path P from s to t such that the driver can see at least one landmark at any point along P and the number of landmarks the driver can stick to is minimized. There are two cases: (a) The same landmark

Minimum energy mobile wireless networks

by Volkan Rodoplu, Teresa H. Meng - IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS , 1999
"... We describe a distributed position-based network protocol optimized for minimum energy consumption in mobile wireless networks that support peer-to-peer communications. Given any number of randomly deployed nodes over an area, we illustrate that a simple local optimization scheme executed at each n ..."
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We describe a distributed position-based network protocol optimized for minimum energy consumption in mobile wireless networks that support peer-to-peer communications. Given any number of randomly deployed nodes over an area, we illustrate that a simple local optimization scheme executed at each

Merrifield-Simmons index and minimum Number of Independent Sets

by Allan Frendrup, Anders Sune Pedersen, Er A. Sapozhenko, Preben Dahl Vestergaard, Allan Frendrup, Anders Sune Pedersen, Alexander A. Sapozhenko, Preben Dahl Vestergaard
"... Merrifield-Simmons index and minimum number of independent sets in short trees by ..."
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Merrifield-Simmons index and minimum number of independent sets in short trees by

MINIMUM NUMBER OF DISTINCT EIGENVALUES OF GRAPHS

by Bahman Ahmadi, Fatemeh Alinaghipour, Michael S. Cavers, Shaun Fallat, Karen Meagher, Shahla Nasserasr , 2013
"... The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to deduce further properties of q(G). It is shown that there is a great number of ..."
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The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to deduce further properties of q(G). It is shown that there is a great number

The minimum number of nonnegative edges in hypergraphs

by Hao Huang , Benny Sudakov - Electron. J. Combin , 2014
"... Abstract An r-unform n-vertex hypergraph H is said to have the Manickam-Miklós-Singhi (MMS) property if for every assignment of weights to its vertices with nonnegative sum, the number of edges whose total weight is nonnegative is at least the minimum degree of H. In this paper we show that for n & ..."
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Abstract An r-unform n-vertex hypergraph H is said to have the Manickam-Miklós-Singhi (MMS) property if for every assignment of weights to its vertices with nonnegative sum, the number of edges whose total weight is nonnegative is at least the minimum degree of H. In this paper we show that for n

Minimum numbers and Wecken theorems in . . . I

by Ulrich Koschorke , 2013
"... ..."
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A problem of Erdös on the minimum number . . .

by Shagnik Das, et al.
"... ..."
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