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

Ken-ichi Kawarabayashi, Bruce Reed
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
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]

Dhia Mahjoub, David W. Matula
2009 Lecture Notes in Computer Science  
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

Nathan Bowler, Johannes Carmesin, Jerzy Wojciechowski, Shadisadat Ghaderi
2020 Electronic Journal of Combinatorics  
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

Alexander Kelmans, Dhruv Mubayi, Benny Sudakov
2001 Electronic Journal of Combinatorics  
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  
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]

Elad Aigner-Horev, Johannes Carmesin, Jan-Oliver Fröhlich
2012 arXiv   pre-print
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  
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

Julia Chuzhoy, Merav Parter, Zihan Tan, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
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

András Frank, Zoltán Szigeti
1995 Mathematical programming  
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

Tapio Rajala
2010 Monatshefte für Mathematik (Print)  
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]

Asaf Ferber, Choongbum Lee, Frank Mousset
2016 arXiv   pre-print
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

David A. Grable
1999 Combinatorica  
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]

Juanjo Rué, Ignasi Sau, Dimitrios M. Thilikos
2012 Lecture Notes in Computer Science  
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

Brett Stevens, Eric Mendelsohn
2004 Theoretical Computer Science  
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

B STEVENS
2004 Theoretical Computer Science  
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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