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Minimum weight

About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.


Papers
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Journal ArticleDOI
01 Jun 1985-Networks
TL;DR: This article considers a generalization which seeks a minimum weight subset υ satisfying the stated conditions where the weights of arcs in are assigned arbitrary integer values.
Abstract: Given a directed graph G(,), the problem of finding a minimum cardinality subset υ ⊆ such that the subgraph, G(,), preserves the reachability properties of G(,) is well known to be difficult. In this article, we consider a generalization which seeks a minimum weight subset υ satisfying the stated conditions where the weights of arcs in are assigned arbitrary integer values. A polynomial-time algorithm is given for the case where the underlying, undirected graph is series-parallel. Naturally, the stated algorithm subsumes the cardinality case on such graphs as well.

14 citations

Journal ArticleDOI
TL;DR: In this article, the minimum weight of the ternary dual codes of each of the four projective planes of order 9 and of the seven affine planes in order 9 was determined.

13 citations

Journal ArticleDOI
TL;DR: An efficient algorithm is presented which generates minimumk-covers continuously as the parameterk ranges over all feasible values, together with a proof of optimality.
Abstract: Consider an edge-weighted graphG = (V, L), and define ak-cover C as a subset of the edgesL such that each vertex inV is incident to at least one edge ofC, and|C| = k. GivenG andk, the problem is to find ak-cover of minimum weight sum. This paper presents characterizations of minimumk-covers, and shows their weight to be convex with the parameterk. An efficient algorithm is presented which generates minimumk-covers continuously as the parameterk ranges over all feasible values, together with a proof of optimality. The computational order of this algorithm is found to be|V| ⋅ |L|2.

13 citations

Book ChapterDOI
17 Aug 2006
TL;DR: It is proved that a code which is similar to the SHA-1 message expansion code has minimum distance at least 82, and that too in just the last 64 of the 80 expanded words.
Abstract: We develop a new technique to lower bound theminimum distance of quasi-cyclic codes with large dimension by reducing the problem to lower bounding the minimum distance of a few significantly smaller dimensional codes. Using this technique, we prove that a code which is similar to the SHA-1 message expansion code has minimum distance at least 82, and that too in just the last 64 of the 80 expanded words. Further the minimum weight in the last 60 words (last 48 words) is at least 75 (52 respectively). We expect our technique to be helpful in designing future practical collision-resistant hash functions. We also use the technique to find the minimum weight of the SHA-1 code (25 in the last 60 words), which was an open problem.

13 citations

Journal Article
TL;DR: In this article, a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton is proposed, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al.
Abstract: We present improvements in finding the LMT-skeleton, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al, and Dickerson and Montague. Our improvements consist of: (1) A criteria is proposed to identify edges in all minimum weight triangulations, which is a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton; (2) A worst-case efficient algorithm is presented for performing one pass of Dickerson and Montague's method (with our new criteria); (3) Improvements in the implementation that may lead to substantial space reduction for uniformly distributed point sets.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202239
202153
202051
201966
201858