7508434
Call routing and the ratcatcher
Suppose we expect there to bep(ab) phone calls between locationsa andb, all choices ofa, b from some setL of locations. We wish to design a network to optimally handle these calls. More precisely, a “routing tree” is a treeT with set of leavesL, in which every other vertex has valency 3. It has “congestion” <k if for every edgee ofT, there are fewer thank calls which will be routed alonge, that is, between locationa, b in different components ofT/e. Deciding if there is a routing tree with congestion <k is NP-hard, but if the pairsab, withp(ab)>0 form the edges of a planar graphG, there is an efficient, strongly polynomial algorithm.This is because the problem is equivalent to deciding if a ratcatcher can corner a rat loose in the walls of a house with floor planG, wherep(ab) is a thickness of the wallab. The ratcatcher carries a noisemaker of powerk, and the rat will not move through any wall in which the noise level is too high (determined by the total thickness of the intervening walls between this one and the noisemaker).It follows that branch-width is polynomially computable for planar graphs—that too is NP-hard for general graphs.
18561897
Excluding infinite minors
Let ? be an infinite cardinal, and let H be either a complete graph with ? vertices, or a tree in which every vertex has valency ?. What can we say about graphs G which (i) have no minor isomorphic to H, or (ii) contain no subgraph which is a subdivision of H?These four questions are answered for each infinite cardinal ?. In each case we find that there corresponds a necessary and sufficient structural condition (or, in some cases, several equivalent conditions) for G not to contain H in the appropriate way. We survey these results and a number of related theorems.
10511288
Clique Minors in Graphs and Their Complements
A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t?1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c=c(t) independent of G such that the complement of G has a minor isomorphic to Ks, where s=?12(1+1/t)n?c?. We prove that Kostochka's conjecture is equivalent to the conjecture of Duchet and Meyniel that every graph with no minor isomorphic to Kt+1 has an independent set of size at least n/t. We deduce that Kostochka's conjecture holds for all integers t?5, and that a weaker form with s replaced by s?=?12(1+1/(2t))n?c? holds for all integers t?1.
2783736
List Edge-Colorings of Series-Parallel Graphs
It is proved that for every integer $k\ge3$, for every (simple) series-parallel graph $G$ with maximum degree at most $k$, and for every collection $(L(e):e\in E(G))$ of sets, each of size at least $k$, there exists a proper edge-coloring of $G$ such that for every edge $e\in E(G)$, the color of $e$ belongs to $L(e)$.
206570580
Sachs' Linkless Embedding Conjecture
Abstract We prove Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link (in the sense of knot theory) if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges. We also show the following: (i) A graph admits such a "linkless" embedding if and only if it admits a "panelled" embedding, one such that every circuit of the graph bounds a disc disjoint from the remainder of the graph. This was a conjecture of Bohme. (ii) An embedding is panelled if and only if for every subgraph, its complement in 3-space has free fundamental group. This extends a theorem of Scharlemann and Thompson, who proved it for planar graphs. (iii) If two panelled embeddings of the same graph are "different," that is, are not related by an orientation-preserving homeomorphism of the 3-space, then there is a subgraph which is a subdivision of K 5 or K 3, 3 such that the two induced embeddings of this subgraph are still different.
33726107
A menger-like property of tree-width: The finite case
The notion of tree-width was introduced by Robertson and Symour. A graph has tree-width ≦ w if it admits a tree-decomposition of tree-width ≦ w. We prove here that if G is finite and has tree-width ≦ w then it admits a tree-decomposition of tree-width ≦ w which satisfies a certain Menger-like condition. This result will be used in a future paper on well-quasi-ordering infinite graphs of bounded tree-width.
12496489
Studying long-term system use
here have been many studies of computer users but few that extend over very long periods. The reasons for this include costs, the quality of the data that can be obtained and satisfactorily analyzed , and the requirement to obtain results in the short term. We were interested in building long-term user models for teaching systems and wished to track the total development of a guru as well as other types of users. Such goals require tracking large numbers of people over a very long period, because guru-level experience takes years to acquire, and it cannot be predicted in advance who will turn out to develop this level of skill. Therefore, to find even one guru may require the tracking of around 20 to 100 users for a year or two. Finding 10 gurus might require 1,000 users. It is possible to observe such numbers over years only by using a method that is very careful about costs. The objective of this article is to present a methodology for monitoring many users in their natural settings over the long term and to give an example of its application to the domain of students learning an editor for three years. We show how data obtained from this methodology permits the construction of individual user models. Monitoring Methodology We developed a monitoring system to study the use of the sam text editor [13]. It is essentially a modeless editor, with most basic commands invoked using the mouse. It also has powerful keyboard commands, issued through the command window, including the usual Unix regular expressions and an elegant interface to the Unix shell. We had a number of design goals for our system, which strongly influenced our methods. First, we were restricted to low system-building costs followed by very low operational costs. Second, the system needed to be highly reliable; it would not be possible to make changes once the monitoring was under way, nor could the immediate availability of people to fix problems during operation be guaranteed. Third, the impact on the computing resources had to be negligible-a degradation in performance during the day was not an option. Fourth, we wanted to give the users some control over their own data, they should be able to read it and delete it if they really wanted. Finally, and most demandingly, we wanted to measure the time of first use of each command, but …
2943319
Thermal unit commitment including optimal AC power flow constraints
The authors propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator time-spanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for the VArs that they can produce, as well as for their real power. Furthermore, although the algorithm is very CPU-intensive, the separation structure of the Lagrangian allows its implementation in parallel computers. Their work builds upon that of Batut and Renaud (1992), as well as that of Baldick (1995).
2733176
The pervasiveness of evolution in GRUMPS software
This paper describes the evolution of the design and implementation of a distributed run-time system that itself is designed to support the evolution of the topology and implementation of an executing, distributed system. The three different versions of the run-time architecture that have been designed and implemented are presented, together with how each architecture addresses the problems of topological and functional evolution. In addition, the reasons for the rapid evolution of the design and implementation of the architecture are also described.From the lessons learned in both evolving the design of the architecture and in trying to provide a run-time system that can support run-time evolution, this paper discusses two generally applicable observations: evolution happens all the time, and it is not possible to anticipate how systems will evolve as designs; and large, run-time systems do not follow a predictable path. In addition to this, rapid prototyping has proved to be extremely useful in the production of the three architectures; this kind of prototyping has been made much easier by designing the core set of Java abstractions in terms of interfaces; and building an architecture that allows as many decisions as possible to be made at run-time which has produced a support system that is more responsive to the user as well as the distributed environment in which it is executing.
10032152
Parallel processing implementation of the unit commitment problem with full AC power flow constraints
The authors describe a parallel implementation of the Lagrangian Relaxation Algorithm with variable duplication for the thermal unit commitment problem. The formulation was previously reported by the authors and allows inclusion of the full nonlinear AC network power flow model, which permits addressing voltage limits, as well as more realistic branch flow limits than is possible with a linear DC flow model. Thus, potential VAr production can be used as another criterion for commitment of otherwise expensive generators in strategic locations. The algorithm is highly parallelizable, and the authors have taken advantage of this in a version currently being developed for the Cornell Theory Center's Velocity AC3 NT cluster.
14857147
An economic analysis of the self commitment of thermal units
Given the load profile of an electricity market and the capabilities of the set of generators supplying power to that market, it is likely that at any given point in time, available supply will exceed demand. If only a subset of generators is required, some method is required to commit and de-commit generators. In the past, system operators have employed a centralized method of unit commitment. Deregulation of the electricity industry throws doubt on the continued suitability of this method due to fairness issues and availability of accurate cost data. This paper examines the performance of decentralized unit commitment, where dispatch of generators is determined by offer curves submitted into a spot market by power producers.