On the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets

2005 ◽  
Vol 21 (3) ◽  
pp. 333-341 ◽  
Author(s):  
Criel Merino ◽  
Gelasio Salazar ◽  
Jorge Urrutia
Keyword(s):  
Minimum Weight ◽  
Intersection Number ◽  
Perfect Matchings ◽  
Point Sets

scholarly journals Packing Plane Perfect Matchings into a Point Set

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Ahmad Biniaz ◽  
Prosenjit Bose ◽  
Anil Maheshwari ◽  
Michiel Smid
Keyword(s):  
Lower Bound ◽  
General Position ◽  
Perfect Matchings ◽  
Point Sets ◽  
Exact Answer ◽  
International Audience ◽  
Point Set

International audience Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? For points in general position we prove the lower bound of &#x230A;log<sub>2</sub>$n$&#x230B;$-1$. For some special configurations of point sets, we give the exact answer. We also consider some restricted variants of this problem.

scholarly journals Point sets with many non-crossing perfect matchings

2018 ◽  
Vol 68 ◽  
pp. 7-33 ◽  
Author(s):  
Andrei Asinowski ◽  
Günter Rote
Keyword(s):  
Perfect Matchings ◽  
Point Sets

DIAMONDS ARE NOT A MINIMUM WEIGHT TRIANGULATION'S BEST FRIEND

2002 ◽  
Vol 12 (06) ◽  
pp. 445-453 ◽  
Author(s):  
PROSENJIT BOSE ◽  
LUC DEVROYE ◽  
WILLIAM EVANS
Keyword(s):  
Polynomial Time ◽  
Minimum Weight ◽  
Connected Subgraph ◽  
Constant Number ◽  
Point Sets ◽  
Expected Number ◽  
Number Of Components ◽  
Best Friend ◽  
Point Set ◽  
Minimum Weight Triangulation

Two recent methods have increased hopes of finding a polynomial time solution to the problem of computing the minimum weight triangulation of a set S of n points in the plane. Both involve computing what was believed to be a connected or nearly connected subgraph of the minimum weight triangulation, and then completing the triangulation optimally. The first method uses the light graph of S as its initial subgraph. The second method uses the LMT-skeleton of S. Both methods rely, for their polynomial time bound, on the initial subgraphs having only a constant number of components. Experiments performed by the authors of these methods seemed to confirm that randomly chosen point sets displayed this desired property. We show that there exist point sets where the number of components is linear in n. In fact, the expected number of components in either graph on a randomly chosen point set is linear in n, and the probability of the number of components exceeding some constant times n tends to one.

scholarly journals Computing Minimum-Weight Perfect Matchings

1999 ◽  
Vol 11 (2) ◽  
pp. 138-148 ◽  
Author(s):  
William Cook ◽  
André Rohe
Keyword(s):  
Minimum Weight ◽  
Perfect Matchings

Further Studies on the Mechanisms for the Antithrombotic Effects of Sulfated Polysaccharides in Rabbits

1988 ◽  
Vol 60 (02) ◽  
pp. 188-192 ◽  
Author(s):  
F A Ofosu ◽  
F Fernandez ◽  
N Anvari ◽  
C Caranobe ◽  
F Dol ◽  
...  
Keyword(s):  
Antithrombin Iii ◽  
Ex Vivo ◽  
Thrombus Formation ◽  
Minimum Weight ◽  
Sulfated Polysaccharides ◽  
Pentosan Polysulfate ◽  
Heparin Cofactor Ii ◽  
Thrombin Inhibition ◽  
The Relationship ◽  
Prothrombin Activation

SummaryA recent study (Fernandez et al., Thromb. Haemostas. 1987; 57: 286-93) demonstrated that when rabbits were injected with the minimum weight of a variety of glycosaminoglycans required to inhibit tissue factor-induced thrombus formation by —80%, exogenous thrombin was inactivated —twice as fast in the post-treatment plasmas as the pre-treatment plasmas. In this study, we investigated the relationship between inhibition of thrombus formation and the extent of thrombin inhibition ex vivo. We also investigated the relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo. Four sulfated polysaccharides (SPS) which influence coagulation in a variety of ways were used in this study. Unfractionated heparin and the fraction of heparin with high affinity to antithrombin III potentiate the antiproteinase activity of antithrombin III. Pentosan polysulfate potentiates the activity of heparin cofactor II. At less than 10 pg/ml of plasma, all three SPS also inhibit intrinsic prothrombin activation. The fourth agent, dermatan sulfate, potentiates the activity of heparin cofactor II but fails to inhibit intrinsic prothrombin activation even at concentrations which exceed 60 pg/ml of plasma. Inhibition of thrombus formation by each sulfated polysaccharides was linearly related to the extent of thrombin inhibition achieved ex vivo. These observations confirm the utility of catalysis of thrombin inhibition as an index for assessing antithrombotic potential of glycosaminoglycans and other sulfated polysaccharides in rabbits. With the exception of pentosan polysulfate, there was no clear relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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