Results 1  10
of
104
Path Set Selection in Mobile Ad Hoc Networks
, 2002
"... Topological changes in mobile ad hoc networks frequently render routing paths unusable. Such recurrent path failures have detrimental effects on the network ability to support QoSdriven services. A promising technique for addressing this problem is to use multiple redundant paths between the source ..."
Abstract

Cited by 67 (6 self)
 Add to MetaCart
Topological changes in mobile ad hoc networks frequently render routing paths unusable. Such recurrent path failures have detrimental effects on the network ability to support QoSdriven services. A promising technique for addressing this problem is to use multiple redundant paths between the source and the destination. However,while multipath routing algorithms can tolerate network failures well,their failure resilience only holds if the paths are selected judiciously. In particular,the correlation between the failures of the paths in a redundant path set should be as small as possible. However,selecting an optimal path set is an NPcomplete problem. Heuristic solutions proposed in the literature are either too complex to be performed in realtime, or too ineffective,or both. This paper proposes a multipath routing algorithm,called Disjoint Pathset Selection Protocol (DPSP),based on a novel heuristic that,in nearly linear time on average,picks a set of highly reliable paths. The convergence to a highly reliable path set is very fast,and the protocol provides flexibility in path selection and routing algorithm. Furthermore,DPSP is suitable for realtime execution,with nearly no message exchange overhead and with minimal additional storage requirements. This paper presents evidence that multipath routing can mask a substantial number of failures in the network compared to single path routing protocols,and that the selection of paths according to DPSP can be beneficial for mobile ad hoc networks,since it dramatically reduces the rate of route discoveries.
A Survey of Graph Pebbling
 Congr. Numer
, 1999
"... We survey results on the pebbling numbers of graphs as well as their historical connection with a numbertheoretic question of Erdös and Lemke. We also present new results on two probabilistic pebbling considerations, first the random graph threshold for the property that the pebbling number of a gr ..."
Abstract

Cited by 39 (14 self)
 Add to MetaCart
(Show Context)
We survey results on the pebbling numbers of graphs as well as their historical connection with a numbertheoretic question of Erdös and Lemke. We also present new results on two probabilistic pebbling considerations, first the random graph threshold for the property that the pebbling number of a graph equals its number of vertices, and second the pebbling threshold function for various natural graph sequences. Finally, we relate the question of the existence of pebbling thresholds to a strengthening of the normal property of posets, and show that the multiset lattice is not supernormal.
Isoperimetric Problems in Discrete Spaces
 Bolyai Soc. Math. Stud
, 1994
"... This paper is a survey on discrete isoperimetric type problems. We present here as some known facts about their solutions as well some new results and demonstrate a general techniques used in this area. The main attention is paid to the unit cube and cube like structures. Besides some applications o ..."
Abstract

Cited by 29 (5 self)
 Add to MetaCart
This paper is a survey on discrete isoperimetric type problems. We present here as some known facts about their solutions as well some new results and demonstrate a general techniques used in this area. The main attention is paid to the unit cube and cube like structures. Besides some applications of the isoperimetric approach are listed too. 1 Introduction This paper is devoted to the discrete isoperimetric problem. This problem may be considered as an analog of the well known continuous problem and has some similar features. The discrete isoperimetric problem began to be studied a very long ago and a lot about it's solutions is known now. If there is the only solution of the continuous version, the discrete one, considered for the unit cube, has generally more solutions with much more rich structure, which have no direct continuous analogs. It is mainly due to the facts that, at first not for all values of cardinality of a subset (which is defined as the number of cube points in the...
List Decoding of qary ReedMuller Codes
 IEEE Trans. Inform. Theory
, 2004
"... The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon codes, which allow polynomials in m variables to encode the message. Using an idea of reducing the multivariate case to univariate case, randomized listdecoding algorithms for ReedMuller codes were given in ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
(Show Context)
The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon codes, which allow polynomials in m variables to encode the message. Using an idea of reducing the multivariate case to univariate case, randomized listdecoding algorithms for ReedMuller codes were given in [1] and [27]. The algorithm in [27] is an improvement of the algorithm in [1], it works for up to E < n(1 − √ 2u/q) errors but is applicable only to codes RMq(u, m) with u < q/2. In this paper, we will propose some deterministic listdecoding algorithms for qary ReedMuller codes. Viewing qary ReedMuller codes as codes from order domains, we present a listdecoding algorithm for qary ReedMuller codes, which is a straightforward generalization of the listdecoding algorithm of ReedSolomon codes in [9]. The algorithm works for up to n(1 − m+1 √ u/q) m − 1 errors, and it is applicable to codes RMq(u, m) with u < q. The algorithm can be implemented to run in time polynomial in the length of the codes. Following [12], we show that qary ReedMuller codes are subfield subcodes of ReedSolomon codes. We then present a second listdecoding algorithm for qary ReedMuller codes. This algorithm works for codes with any rates, and achieves an errorcorrection bound n(1 − √ (n − d)/n) − 1. So the second algorithm achieves a better errorcorrection bound than the algorithm in [27], since when u is small, n(1 − √ (n − d)/n) = n(1 − √ u/q). The implementation of the second algorithm requires O(n) field operations in Fq and O(n3) field operations in Fqm under some assumption. Also, we prove that qary ReedMuller codes can be described as onepoint AG codes. And using the algorithm of AG codes in [9], we give a third listdecoding
Face vectors of flag complexes
"... Abstract. A conjecture of Kalai and Eckhoff that the face vector of an arbitrary flag complex is also the face vector of some particular balanced complex is verified. 1. ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
(Show Context)
Abstract. A conjecture of Kalai and Eckhoff that the face vector of an arbitrary flag complex is also the face vector of some particular balanced complex is verified. 1.
Thresholds for Families of Multisets, With an Application to Graph Pebbling
, 2000
"... In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász's version of the KruskalKatona Theorem and an analog of the Bollob asThomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. I ..."
Abstract

Cited by 20 (15 self)
 Add to MetaCart
(Show Context)
In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász's version of the KruskalKatona Theorem and an analog of the Bollob asThomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. In addition, we improve both the lower and upper bounds for the `random pebbling' threshold of the sequence of paths.
Generalized Hamming weights of qary ReedMuller codes
 IEEE Trans. Inform. Theory
, 1998
"... Abstract The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as the qary ReedMuller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain c ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
Abstract The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as the qary ReedMuller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition. 1
TRACES OF FINITE SETS: EXTREMAL PROBLEMS AND GEOMETRIC APPLICATIONS
, 1992
"... Given a hypergraph H and a subset S of its vertices, the trace of H on S is defined as HS = {E ∩ S: E ∈ H}. The Vapnik–Chervonenkis dimension (VCdimension) of H is the size of the largest subset S for which HS has 2 S edges. Hypergraphs of small VCdimension play a central role in many areas o ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
Given a hypergraph H and a subset S of its vertices, the trace of H on S is defined as HS = {E ∩ S: E ∈ H}. The Vapnik–Chervonenkis dimension (VCdimension) of H is the size of the largest subset S for which HS has 2 S edges. Hypergraphs of small VCdimension play a central role in many areas of statistics, discrete and computational geometry, and learning theory. We survey some of the most important results related to this concept with special emphasis on (a) hypergraph theoretic methods and (b) geometric applications.