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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
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We consider the following problem, which is called the half integral parity disjoint paths packing problem. ...
paths packing problem, i.e., without the parity requirement. ...
parities of half-integral disjoint paths packing. ...
doi:10.1137/1.9781611973068.128
fatcat:unk4ykwdjne3jdjaieltvvr2ri
Experimental Study of Independent and Dominating Sets in Wireless Sensor Networks Using Graph Coloring Algorithms
[chapter]
2009
Lecture Notes in Computer Science
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Furthermore, if we relax the full domination constraint then we obtain a partitioning of the network into 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 . ...
doi:10.1007/978-3-642-03417-6_4
fatcat:hbvpocsncbcwhmic75suu76asq
The Almost Intersection Property for Pairs of Matroids on Common Groundset
2020
Electronic Journal of Combinatorics
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Theorem 4 . 2 . 42 If M and N are 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. ...
doi:10.37236/8881
fatcat:cdpjzy5ennegzl5bmy4ohxnp6a
Asymptotically Optimal Tree-Packings in Regular Graphs
2001
Electronic Journal of Combinatorics
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Clearly, an $n$ vertex graph contains at most $n/t$ vertex 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. ...
doi:10.37236/1582
fatcat:zpjps4qcj5allnnf3myfxyxr24
Page 4818 of Mathematical Reviews Vol. , Issue 83m
[page]
1983
Mathematical Reviews
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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 @. ...
Infinite matroid union
[article]
2012
arXiv
pre-print
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We introduce a superclass of the finitary matroids, the 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. ...
arXiv:1111.0602v2
fatcat:5js3g4uqabhixjzgjgciw557xq
Page 604 of Mathematical Reviews Vol. , Issue 93b
[page]
1993
Mathematical Reviews
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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. ...
On Packing Low-Diameter Spanning Trees
2020
International Colloquium on Automata, Languages and Programming
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This immediately gives a tree 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. ...
doi:10.4230/lipics.icalp.2020.33
dblp:conf/icalp/ChuzhoyPT20
fatcat:7gtbcnxbsrbglnfrxo7ccyr3qu
A note on packing paths in planar graphs
1995
Mathematical programming
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Analogously to Seymour's approach, we actually prove a theorem on 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 ( ...
doi:10.1007/bf01585937
fatcat:a5njs2efrjhojfipc66snef55i
Comparing the Hausdorff and packing measures of sets of small dimension in metric spaces
2010
Monatshefte für Mathematik (Print)
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We give a new estimate for the ratio of s-dimensional Hausdorff measure H s and (radius-based) 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. ...
doi:10.1007/s00605-010-0271-3
fatcat:dhwkvjnny5hghgiqr22lhkrule
Packing spanning graphs from separable families
[article]
2016
arXiv
pre-print
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The proof uses the local resilience of random graphs and a special multi-stage 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 ...
arXiv:1512.08701v2
fatcat:7j2bjum6onbl7h2jgcqe553dfy
More-Than-Nearly-Perfect Packings and Partial Designs
1999
Combinatorica
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1)+o(1) uncovered t-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). ...
doi:10.1007/s004930050053
fatcat:p7qr5nq5ifb3xlwooqjs2tmduq
Dynamic Programming for H-minor-free Graphs
[chapter]
2012
Lecture Notes in Computer Science
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We show that the separators of such decompositions have connected 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. ...
doi:10.1007/978-3-642-32241-9_8
fatcat:dbkudlpydvdbll6m26vexn7pru
Packing arrays
2004
Theoretical Computer Science
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We introduce the consideration of a 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. ...
doi:10.1016/j.tcs.2003.06.004
fatcat:skcaqdvfvbfpjls4s5dwkempzu
Packing arrays
2004
Theoretical Computer Science
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We introduce the consideration of a 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. ...
doi:10.1016/s0304-3975(04)00125-2
fatcat:s2qwkhg6h5cnxib3l2efy2znd4
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