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A Nearly Linear Time Algorithm For The Half Integral Parity Disjoint Paths Packing Problem
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We consider the following problem, which is called the half integral parity

doi:10.1137/1.9781611973068.128
fatcat:unk4ykwdjne3jdjaieltvvr2ri
*disjoint*paths*packing*problem. ... paths*packing*problem, i.e., without the parity requirement. ... parities of half-integral*disjoint*paths*packing*. ...##
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Experimental Study of Independent and Dominating Sets in Wireless Sensor Networks Using Graph Coloring Algorithms
[chapter]

2009
*
Lecture Notes in Computer Science
*

Furthermore, if we relax the full domination constraint then we obtain a partitioning of the network into

doi:10.1007/978-3-642-03417-6_4
fatcat:hbvpocsncbcwhmic75suu76asq
*disjoint*dominating and*nearly*-dominating*sets*of*nearly*equal size, providing better redundancy ... The*disjoint*maximal independent*sets*constitute a collection of*disjoint*dominating*sets*that offer good network coverage. ...*Nearly*-Equal Sized Independent*Sets*Collection of*Disjoint*Dominating*Sets*Node*Packing*in the Independent*Sets*We consider r=0.12 with several n values as depicted in Table 4 . ...##
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The Almost Intersection Property for Pairs of Matroids on Common Groundset

2020
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Electronic Journal of Combinatorics
*

Theorem 4 . 2 . 42 If M and N are

doi:10.37236/8881
fatcat:cdpjzy5ennegzl5bmy4ohxnp6a
*nearly*finitary, then M ∨ N is a*nearly*finitary matroid. Theorem 4 . 3 . 43 If M and N are*nearly*finitary, then (M, N ) has the*Packing*/Covering Property. Proof. ... For the rest of this section assume that M and N are matroids on a common ground*set*E.A*packing*for (M, N ) is a pair (S, T ) of*disjoint*subsets of E such that cl M (S) = cl N (T ) = E. ...##
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Asymptotically Optimal Tree-Packings in Regular Graphs

2001
*
Electronic Journal of Combinatorics
*

Clearly, an $n$ vertex graph contains at most $n/t$ vertex

doi:10.37236/1582
fatcat:zpjps4qcj5allnnf3myfxyxr24
*disjoint*trees isomorphic to $T$. ... that for every $\epsilon >0$, there exists a $D(\epsilon,t)>0$ such that, if $d>D(\epsilon,t)$ and $G$ is a simple $d$-regular graph on $n$ vertices, then $G$ contains at least $(1-\epsilon)n/t$ vertex*disjoint*... Then G contains at least (1 − )n/t vertex*disjoint*copies of T . the electronic journal of combinatorics 8 (2001), #R38 A matching in H is a*set*of pairwise*disjoint*edges of H. ...##
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Page 4818 of Mathematical Reviews Vol. , Issue 83m
[page]

1983
*
Mathematical Reviews
*

D. 83m:05044

*Packing**nearly**disjoint**sets*. Combinatorica 2 (1982), no. 1, 91-97. ... The proof actually provides an algorithm for finding [|@|/n| pairwise*disjoint**sets*in @. ...##
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Infinite matroid union
[article]

2012
*
arXiv
*
pre-print

We introduce a superclass of the finitary matroids, the

arXiv:1111.0602v2
fatcat:5js3g4uqabhixjzgjgciw557xq
*nearly*finitary matroids, and prove that the union of two*nearly*finitary matroids is a*nearly*finitary matroid. ... We then extend the base*packing*theorem for finite matroids to finite families of co-finitary matroids. ... Base*packing*in co-finitary matroids In this section, we prove Theorem 1.4, which is a base*packing*theorem for co-finitary matroids. ...##
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Page 604 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

H is
called

*nearly**disjoint*if |AN B| <1 for all distinct A,B € E(A). The Erdés-Faber-Lovasz conjecture is the following: If H is*nearly**disjoint*on a*set*of size n then x'(H) <n. ... In this paper it is shown that if H is a*nearly**disjoint*hypergraph on a*set*of size n then x'(H) < (1+ 0(1))n. The proof of this result is based on a generalization of a theorem of N. ...##
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On Packing Low-Diameter Spanning Trees

2020
*
International Colloquium on Automata, Languages and Programming
*

This immediately gives a tree

doi:10.4230/lipics.icalp.2020.33
dblp:conf/icalp/ChuzhoyPT20
fatcat:7gtbcnxbsrbglnfrxo7ccyr3qu
*packing*of Ω(k/log n) edge-*disjoint*trees of diameter at most O(k^(D(D+1)/2)). ... We also show that these two results are*nearly*tight for graphs with a small diameter: we show that there are k-edge connected graphs of diameter 2D, such that any*packing*of k/α trees with edge-congestion ... A key tool for leveraging high edge connectivity of a given graph is tree*packing*: a large collection of spanning trees that are (*nearly*) edge-*disjoint*. ...##
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A note on packing paths in planar graphs

1995
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Mathematical programming
*

Analogously to Seymour's approach, we actually prove a theorem on

doi:10.1007/bf01585937
fatcat:a5njs2efrjhojfipc66snef55i
*packing*cuts in an arbitrary graph and then the planar edge-*disjoint*paths case is obtained by planar dualization. ... Penn proved that the cut criterion is su cient for the existence of a near-complete*packing*of paths. ... In other words, the theorem says that there is a*packing*of F -good cuts which is*nearly*complete in the sense that each edge of K i (i = 0; : : : ; k) is covered and each but at most one edge of F j ( ...##
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Comparing the Hausdorff and packing measures of sets of small dimension in metric spaces

2010
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Monatshefte für Mathematik (Print)
*

We give a new estimate for the ratio of s-dimensional Hausdorff measure H s and (radius-based)

doi:10.1007/s00605-010-0271-3
fatcat:dhwkvjnny5hghgiqr22lhkrule
*packing*measure P s of a*set*in any metric space. ... As an immediate consequence we improve the upper bound for the lower s-density of such*sets*in R n . ... A δ-*packing*of a*set*E ⊂ X is a countable collection of*disjoint*balls of radii at most δ and with centers in E. ...##
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Packing spanning graphs from separable families
[article]

2016
*
arXiv
*
pre-print

The proof uses the local resilience of random graphs and a special multi-stage

arXiv:1512.08701v2
fatcat:7j2bjum6onbl7h2jgcqe553dfy
*packing*procedure. ... The result also implies approximate versions of the Oberwolfach problem and of the Tree*Packing*Conjecture of Gyárfás (1976) for the case that all trees have maximum degree at most Δ. ... A well-known result of Böttcher, Hladký, Piguet, and Taraz [8] shows that in this*setting*, one can achieve*nearly*perfect*packings*of trees, provided that the size of the trees is bounded away from n ...##
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More-Than-Nearly-Perfect Packings and Partial Designs

1999
*
Combinatorica
*

1)+o(1) uncovered t-

doi:10.1007/s004930050053
fatcat:p7qr5nq5ifb3xlwooqjs2tmduq
*sets*, improving the earlier o(n t ) result. P v2V (H ) deg(v) = kjE(H)j=jV ( ... edges (*packings*) which cover all but o(n) of the n vertices. ... The connection with*packings*in hypergraphs is that each (*nearly*-perfect) partial S(t; k; n) corresponds to a (*nearly*-perfect)*packing*in the following hypergraph, which we denote by H(t; k; n). ...##
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Dynamic Programming for H-minor-free Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

We show that the separators of such decompositions have connected

doi:10.1007/978-3-642-32241-9_8
fatcat:dbkudlpydvdbll6m26vexn7pru
*packings*whose behavior can be described in terms of a combinatorial object called'-triangulation. ... A configuration in F is a*set*of vertex-*disjoint*subgraphs F = {F 1 , . . . , F`} of F . ... We say that a*packing*(that is, a collection of pairwise*disjoint*non-empty blocks) of the disc D k is an`-*packing*if and only if G(⇧) does not contain K`+ 1 as a subgraph. ...##
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Packing arrays

2004
*
Theoretical Computer Science
*

We introduce the consideration of a

doi:10.1016/j.tcs.2003.06.004
fatcat:skcaqdvfvbfpjls4s5dwkempzu
*set*of*disjoint*rows in a*packing*array which allows these constructions and additionally gives a new upper bound on the size of all*packing*arrays. ... We develop general direct and recursive constructions and upper bounds on the sizes of*packing*arrays. ... Tables of upper and lower bounds We include here tables showing the values for the upper and lower bounds on*packing*arrays. ...##
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Packing arrays

2004
*
Theoretical Computer Science
*

We introduce the consideration of a

doi:10.1016/s0304-3975(04)00125-2
fatcat:s2qwkhg6h5cnxib3l2efy2znd4
*set*of*disjoint*rows in a*packing*array which allows these constructions and additionally gives a new upper bound on the size of all*packing*arrays. ... We develop general direct and recursive constructions and upper bounds on the sizes of*packing*arrays. ... Tables of upper and lower bounds We include here tables showing the values for the upper and lower bounds on*packing*arrays. ...
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