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Compact Forbidden-Set Routing [chapter]

Bruno Courcelle, Andrew Twigg
STACS 2007  
Lemma 1 We have forbidden-set distance labels J(x) of size O(k 2 ht(t) log n) bits. Q: How to replace the height ht(t) by log n ? A: Using balanced terms  ...  Forbidden edges For shortest paths leaving a set X, we replace their corresponding subterms with shortcut edges in the graph representation of a term, and stored in labels assigned to vertices of G. d(  ...  Conclusion Forbidden-set distance labelling for mcwd graphs "Distance labelling with obstacles" Can obtain a compact routing scheme Techniques Use algebraic representation of graphs Better describes how  ... 
doi:10.1007/978-3-540-70918-3_4 dblp:conf/stacs/CourcelleT07 fatcat:zd3ljq4ep5espbppmg7mhfhnom

f-Sensitivity Distance Oracles and Routing Schemes [chapter]

Shiri Chechik, Michael Langberg, David Peleg, Liam Roditty
2010 Lecture Notes in Computer Science  
The paper also considers f -sensitive compact routing schemes, namely, routing schemes that avoid a given set of forbidden (or failed) edges.  ...  Moreover, those oracles support forbidden sets F of size |F | ≤ 2.  ...  Theorem 1.2 There exists a 2-sensitive compact routing scheme that given a message M at a source vertex s and a destination t, in the presence of a forbidden edge set F of size at most 2 (unknown to s)  ... 
doi:10.1007/978-3-642-15775-2_8 fatcat:g3sneyv2i5gtnkketjj67q7lmm

f-Sensitivity Distance Oracles and Routing Schemes

Shiri Chechik, Michael Langberg, David Peleg, Liam Roditty
2011 Algorithmica  
The paper also considers f -sensitive compact routing schemes, namely, routing schemes that avoid a given set of forbidden (or failed) edges.  ...  Moreover, those oracles support forbidden sets F of size |F | ≤ 2.  ...  Theorem 1.2 There exists a 2-sensitive compact routing scheme that given a message M at a source vertex s and a destination t, in the presence of a forbidden edge set F of size at most 2 (unknown to s)  ... 
doi:10.1007/s00453-011-9543-0 fatcat:hpy6n45te5fufduswlg45djtuq

Forbidden-set distance labels for graphs of bounded doubling dimension

Ittai Abraham, Shiri Chechik, Cyril Gavoille, David Peleg
2010 Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10  
The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by α.  ...  Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in time polynomial in the length of the labels, a 1 + stretch approximation  ...  Courcelle for helpful discussions about labeling schemes in the forbidden-set setting.  ... 
doi:10.1145/1835698.1835743 dblp:conf/podc/AbrahamCGP10 fatcat:olj5dfhklnaypa2v546luzh4ca

Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension

Ittai Abraham, Shiri Chechik, Cyril Gavoille, David Peleg
2016 ACM Transactions on Algorithms  
The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by α.  ...  Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in time polynomial in the length of the labels, a 1 + stretch approximation  ...  Courcelle for helpful discussions about labeling schemes in the forbidden-set setting.  ... 
doi:10.1145/2818694 fatcat:m2dn3i42zzeiteai3jlq3c7hpm

Page 1611 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Summary: “Interval routing is a compact way of representing routing tables on a graph.  ...  The graph sandwich problem for 1-join composition is defined as follows: Given a vertex set V, a forced edge set E', and a forbidden edge set E°, is there a graph G =(V,E) such that E! C E and EN E?  ... 

Forbidden-area avoidance with spacing technique for layout optimization

Shi C. Shi, Alfred K. Wong, Tung-Sang Ng, Lars W. Liebmann
2004 Design and Process Integration for Microelectronic Manufacturing II  
Examples show that the proposed method can avoid most forbidden areas in the layout after normal routing.  ...  In this paper, a pitch optimization method applied in the post-routing phase is proposed to avoid the forbidden areas.  ...  requirement of avoiding forbidden areas in the layout challenges the physical design automation, especially in routing.  ... 
doi:10.1117/12.533640 fatcat:jta7w6wyd5e6zjkzpqdhxr6cfy

Name Independent Fault Tolerant Routing Scheme [article]

Alkida Balliu, Dennis Olivetti
2017 arXiv   pre-print
Given a set F of faulty (or forbidden) edges, the goal is to route from a source node s to a target t avoiding the forbidden edges in F.  ...  In particular, we present a name-independent routing scheme able to handle any set F of forbidden edges in |F|+1 connected graphs.  ...  For an overview on compact routing and compact network data structures, see [8, 10] .  ... 
arXiv:1704.06078v3 fatcat:jziauwvvmffudpfof2zran7obu

Scheduling periodic messages on a shared link [article]

Maël Guiraud, Yann Strozecki
2022 arXiv   pre-print
The analysis of Compact Pairs relies on the evaluation of the number of forbidden meta-offsets.  ...  The same offsets are also forbidden by the choice of o as offset for i, hence at most 3τ − 1 new offsets are forbidden, that is FO r 1 − r 0 > 0 Fig. 3 :Lemma 3 1033 Fig. 3: The compact pair (0, 1) with  ... 
arXiv:2002.07606v5 fatcat:fiqnvmdnbfavpeeyyldfcomq54

Connectivity check in 3-connected planar graphs with obstacles

Bruno Courcelle, Cyril Gavoille, Mamadou Moustapha Kanté, Andrew Twigg
2008 Electronic Notes in Discrete Mathematics  
A connectivity query asks whether there exists in the given graph a path linking u and v that avoids a set F of edges and a set X of vertices.  ...  As surveyed in [8] many problems including routing and distance computation can be achieved using compact labels.  ...  Courcelle and Twigg studied in [4] the forbidden-set labelling problem, where in addition to source and destination, the query algorithm is given a set of failed nodes and edges and it must construct  ... 
doi:10.1016/j.endm.2008.06.030 fatcat:iwpmuccqobfkjcmqqyyimavhcy

Page 4541 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
The major problems that are addressed in this part are circuit partitioning, placement problems, routing and compaction.  ...  The characterization is given in terms of a set of forbidden b/w subgraphs, the absence of which is necessary and sufficient for one-page b/w embedding.  ... 

Solving an urban waste collection problem using ants heuristics

Joaquín Bautista, Elena Fernández, Jordi Pereira
2008 Computers & Operations Research  
We present the model that we have built for the problem, which results after an appropriate transformation of the problem into a node routing one.  ...  The basic nature of the considered problem is that of a capacitated arc routing problem, although it has several specific characteristics, mainly derived from traffic regulations.  ...  In this work we build a model for the Mixed Capacitated Arc Routing Problem (MCARP) where forbidden turns are taken into account in the set of constraints instead of penalizing forbidden turns via the  ... 
doi:10.1016/j.cor.2007.01.029 fatcat:tdv2ehvfxjfutilvei63yry2jq

A novel timing-driven global routing algorithm considering coupling effects for high performance circuit design

Jingyu Xu, Xianlong Hong, Tong Jing, Yici Cai, Jun Gu
2003 Proceedings of the 2003 conference on Asia South Pacific design automation - ASPDAC  
In this paper, we propose a timing-driven global routing algorithm with consideration of coupling effects.  ...  The coupling effects have brought new challenges to routing algorithms on both delay estimation and optimization.  ...  Note that forbidden nets and un-forbidden nets are transferable.  ... 
doi:10.1145/1119772.1119958 dblp:conf/aspdac/XuHJCG03 fatcat:2a56xhaw2nb4jgdmc7mffqrz4q

Fault-Tolerant Labeling and Compact Routing Schemes [article]

Michal Dory, Merav Parter
2021 arXiv   pre-print
This scheme is based on the notion of linear sketches of [Ahn et al., SODA '12]. – For k≥ 1, there is a randomized routing scheme that routes a message from s to t in the presence of a set F of faulty  ...  Since their introduction by [Courcelle, Twigg, STACS '07], compact FT labeling schemes have been devised only for a limited collection of graph families.  ...  formulations of forbidden-set labeling and routing schemes by Courcelle et al.  ... 
arXiv:2106.00374v1 fatcat:wfgpkcdqdzb5zkh4crwjk65loa

Survey Article: Consequences of some outerplanarity extensions

L. Boza, E.M. Fedriani, J. Núñez
2012 Rocky Mountain Journal of Mathematics  
K VAP (S(1)) is the set {G W : (G, W ) ∈ L 1 (S(1))}, for any compact surface S.  ...  ), it is proved that the minimal set of forbidden minors for graph embeddings with no vertex accumulation point in non-compact surfaces is finite, something that we are about to recall for infinite graphs  ... 
doi:10.1216/rmj-2012-42-4-1073 fatcat:zwe3kkq6qzdpvac3hxmjrzw4rq
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