Simpler Self-reduction Algorithm for Matroid Path-width

The "Art of Trellis Decoding" Is Fixed-Parameter Tractable

Given n subspaces of a finite-dimensional vector space over a fixed finite field F, we wish to find a linear layout V1, V2, . . . , Vn of the subspaces such that dim((V1+V2+· · ·+Vi)∩(Vi+1+· · ·+Vn)) ≤ k for all i; such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the path-width of an F-represented matroid i...

Constructive algorithm for path-width of matroids

Ascending Auctions and Linear Programming∗

Based on the relationship between dual variables and sealed-bid Vickrey auction payments (established by Bikhchandani and Ostroy), we consider simpler, specific formulations for various environments. For some of those formulations, we interpret primal-dual algorithms as ascending auctions implementing the Vickrey payments. We focus on three classic optimization problems: assignment, matroid, an...

Constructive characterizations of 3-connected matroids of path width three

A matroid M is sequential or has path width 3 if M is 3-connected and its ground set has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . , ek}, {ek+1, ek+2, . . . , en}) is a 3-separation for all k in {3, 4, . . . , n − 3}. This paper proves that every sequential matroid is easily constructible from a uniform matroid of rank or corank two by a sequence...

Partial tracks, characterizations and recognition of graphs with path-width at most two

Nancy G. Kinnersley and Michael A. Langston has determined [3] the excluded minors for the class of graphs with path-width at most two. Here we give a simpler presentation of their result. This also leads us to a new characterization, and a linear time recognition algorithm for graphs width path-width at most two. 1 History and introduction Based on the seminal work of Seymour and Robertson [4]...