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Universal maximal packing functions of graphs

1996
*
Discrete Mathematics
*

We consider the existence

doi:10.1016/0012-365x(95)00097-g
fatcat:fm7t4mxlzfgwdf7vyvwqnddahe
*of**universal**maximal**packing**functions*, i.e.*maximal**packing**functions*(MPFs) whose convex combinations with all other MPFs are themselves MPFs. ... A*packing**function**of*a*graph*G = (V, E) is a*function*f: V --* [0, 1] such that for each v ~ V, denotes the closed neighbourhood*of*vertex v). ... The work was completed while the first author was enjoying the hospitality*of*the*University**of*South Africa. ...##
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Page 51 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

We consider the existence

*of**universal**maximal**packing**functions*, i.e.*maximal**packing**functions*(MPFs) whose convex combinations with all other MPFs are themselves MPFs.” ... (SA-SAFR-A; Pretoria)*Universal**maximal**packing**functions**of**graphs*. (English summary) Discrete Math. 159 (1996), no. 1-3, 57-68. ...##
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Optimal Information Rate of Secret Sharing Schemes on Trees

2013
*
IEEE Transactions on Information Theory
*

Secret sharing scheme; information rate;

doi:10.1109/tit.2012.2236958
fatcat:cvlehsqmgrbybofdm3dbec4kue
*graph*; fractional*packing*and cover; entropy method. ... Canada Research Chair*of*Computational and Discrete Geometry at the Simon Fraser*University*, BC, Canada, since 2005. ... a*maximal*weight*function*. ...##
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Optimal information rate of secret sharing schemes on trees
[article]

2013
*
arXiv
*
pre-print

Our result follows from a lower and an upper bound on the information rate that applies for any

arXiv:1302.4609v1
fatcat:is4p7zlnxjhsvfukejj3aswxje
*graph*and happen to coincide for trees because*of*a correspondence between the size*of*the largest core and ... We determine this value for all trees: it is 1/(2-1/c), where c is the size*of*the largest core*of*the tree. ... a*maximal*weight*function*. ...##
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Mining protein family specific residue packing patterns from protein structure graphs

2004
*
Proceedings of the eighth annual international conference on Computational molecular biology - RECOMB '04
*

Avg #

doi:10.1145/974614.974655
dblp:conf/recomb/HuanWBSPT04
fatcat:mx3mx33fobcwxitykeh4qj3yme
*of*edges per residue Edge length prune (Angstrom) Avg vertex degree*of**graph*as*function**of*edge length 12/29/2005 7 The*UNIVERSITY**of*NORTH CAROLINA at CHAPEL HILL*Graph*Database Mining -Problem ... (CAM)*of*a*graph*G is the*maximal*adjacency matrix for G under a total ordering defined on adjacency matrices. ... A group*of*family specific motifs are identified and some*of*them correlate well with the know*function**of*group*of*proteins studied. ...##
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A nonsmooth program for jamming hard spheres
[article]

2012
*
arXiv
*
pre-print

We propose an algorithm for the

arXiv:1209.4053v1
fatcat:rkgjpatv5fd7xi6q45g6h3l5ku
*maximization**of*this*maximal*radius*function*and present examples for 5 - 8 disks in the unit square and 4 - 6 spheres in the unit cube. ... We present a nonsmooth*function*whose local extrema are the radii*of*jammed*packings*(where no subset*of*spheres can be moved keeping all others fixed) and show that for a fixed number*of*spheres there ... Boris Okun and Michael Hero (Department*of*Mathematical Sciences,*University**of*Wisconsin -Milwaukee) and Michael Monagan (Department*of*Mathematics, Simon Fraser*University*, Burnaby, British Columbia) ...##
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Fractional edge domination in graphs

2009
*
Applicable Analysis and Discrete Mathematics
*

The authors are thankful to the Department

doi:10.2298/aadm0902359a
fatcat:gn7lamz4jvgdbhgzexdeivwaru
*of*Science and Technology, New Delhi for its support through the Project SR/S4/MS/282/05. ... p f (G) = min{|g| : g is a*maximal*edge*packing**function**of*G} and P f (G) = max{|g| : g is a*maximal*edge*packing**function**of*G}. Observation 2.5. ... Characterize*graphs*G for which the space*of*all*maximal*edge irredundant*functions*is compact. Problem 3.5. ...##
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Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

2007
*
Algorithmica
*

We obtain faster algorithms for problems such as r-dimensional matching, r-set

doi:10.1007/s00453-007-9146-y
fatcat:kxt6holtirftfccq46oluw2yc4
*packing*,*graph**packing*, and*graph*edge*packing*when the size k*of*the solution is considered a parameter. ... We first establish a general framework for finding and exploiting small problem kernels (*of*size polynomial in k). Previously such a kernel was known only for triangle*packing*. ... We then have the following lemma, analogous to Lemma 5: Lemma 6 For the problems r-Set*Packing*,*Graph**Packing*, and*Graph*Edge-*Packing*, if S ⊆ A and K is the output*of*the*function*Kernel-Construct(S), ...##
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Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
[chapter]

2004
*
Lecture Notes in Computer Science
*

We obtain faster algorithms for problems such as r-dimensional matching, r-set

doi:10.1007/978-3-540-30140-0_29
fatcat:vg5dk5mdvrfxvnycgjfszlfjg4
*packing*,*graph**packing*, and*graph*edge*packing*when the size k*of*the solution is considered a parameter. ... We first establish a general framework for finding and exploiting small problem kernels (*of*size polynomial in k). Previously such a kernel was known only for triangle*packing*. ... We then have the following lemma, analogous to Lemma 5: Lemma 6 For the problems r-Set*Packing*,*Graph**Packing*, and*Graph*Edge-*Packing*, if S ⊆ A and K is the output*of*the*function*Kernel-Construct(S), ...##
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Arbitrary Overlap Constraints in Graph Packing Problems
[article]

2016
*
arXiv
*
pre-print

Let V^r be all possible subsets

arXiv:1601.03676v1
fatcat:o3bp2ri7tvfermuuxwynljmria
*of*vertices*of*V(G) each*of*size at most r, and α: V^r ×V^r →{0,1} be a*function*. ... The Π-*Packing*with α()-Overlap problem seeks at least k induced subgraphs in a*graph*G subject to: (i) each subgraph has at most r vertices and obeys a property Π, and (ii) for any pair H_i,H_j, with i ... In this work, we introduce the r-Set*Packing*and Π-Set*Packing*with α()-Overlap problems as more*universal*versions for the problem*of**packing**graphs*and sets subject to overlap constraints modeled by ...##
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On packing bipartite graphs

1992
*
Combinatorica
*

A theorem

doi:10.1007/bf01285818
fatcat:ibasee5v4jdybaoyqyv2bawpym
*of*Catlin, Spencer and Sauer gives a su cient condition for the existence*of**packing*in terms*of*the product*of*the*maximal*degrees*of*G and H. We improve this theorem for bipartite*graphs*. ... G and H, two simple*graphs*, can be*packed*if G is isomorphic to a subgraph*of*H, the complement*of*H. ... The following few theorems give su cient conditions on the number*of*edges for the existence*of*a*packing*. (ii) If G; H 2 B u;w and jE(G)jjE(H)j < uw, then G and H can be*packed*as bipartite*graphs*. ...##
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Packing functions and graphs with perfect closed neighbourhood matrices
[article]

2018
*
arXiv
*
pre-print

In this work we consider a straightforward linear programming formulation

arXiv:1812.09422v1
fatcat:clap6u63gjbrzjqdh6b2bgwty4
*of*the recently introduced {k}-*packing**function*problem in*graphs*, for each fixed value*of*the positive integer number k. ... We present a necessary and sufficient condition for a*graph*to have a clique-node closed neighbourhood matrix. Finally, we study the perfection*of*the*graph**of**maximal*cliques associated to N[G]. ... Limited*packing**functions*For a*graph*G = (V, E) and a positive integer k, a*function*f : V → Z + is a {k}-*packing**function**of*G [9] , if for each node v ∈ V , f (N [v]) = w∈N [v] f (w) ≤ k. ...##
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Covering and Packing in Linear Space
[chapter]

2010
*
Lecture Notes in Computer Science
*

Given a family

doi:10.1007/978-3-642-14165-2_61
fatcat:udxf6oa5onclxk5p6yyrygxnxy
*of*subsets*of*an n-element*universe*, the kcover problem asks whether there are k sets in the family whose union contains the*universe*; in the k-*packing*problem the sets are required to be ... Thus, for instance, the chromatic or domatic number*of*an n-vertex*graph*can be found in time within a polynomial factor*of*2 n and space proportional to the number*of**maximal*independent sets, O(1.442 ... This bottleneck can be removed by taking a more balanced scheme with n 1 and n 2 about equal, yielding time and space O * (2 n/2 ) for each*of*the O * (2 n/2 ) processors. ...##
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Covering and packing in linear space

2011
*
Information Processing Letters
*

Given a family

doi:10.1016/j.ipl.2011.08.002
fatcat:rj32rkvxknefnerpdocpregzy4
*of*subsets*of*an n-element*universe*, the kcover problem asks whether there are k sets in the family whose union contains the*universe*; in the k-*packing*problem the sets are required to be ... Thus, for instance, the chromatic or domatic number*of*an n-vertex*graph*can be found in time within a polynomial factor*of*2 n and space proportional to the number*of**maximal*independent sets, O(1.442 ... This bottleneck can be removed by taking a more balanced scheme with n 1 and n 2 about equal, yielding time and space O * (2 n/2 ) for each*of*the O * (2 n/2 ) processors. ...##
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Optimal packings of up to six equal circles on a triangular flat torus

2011
*
Journal of Geometry
*

The unique globally

doi:10.1007/s00022-011-0099-6
fatcat:stk5miywnjdgrfbd22s7vz72iq
*maximally*dense*packing**of*n − 1 circles on the standard triangular torus is congruent to C with one circle removed. ... Let n > 1 be a triangular*packing*number so that n − 1 is not a triangular*packing*number and C be the*packing**of*n circles on the standard triangular torus that lift to the triangular close*packing*in ... Some*packings*are local maximums*of*the density*function*. ...
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