43559428
Planar Separators
The authors give a short proof of a theorem of Lipton and Tarjan, that, for every planar graph with n > 0 vertives, there is a partition (A, B, C,) of its vertex set such that $|A|, |B| < \frac{2}{3}n, |C| \geq 2(2n)^{1/2},$ and no vertex in A is adjacent to any vertex in B. Secondly, they apply the same technique more carefully to deduced that, in fact, such a partition (A, B, C) exists with $|A|, |B| < \frac{2}{3}n, |C| \geq 2(2n)^{1/2};$ this improves the best previously known result. An analogous result holds when the vertices or edges are weighted.
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.
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.
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 $L(e)$.
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.
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.
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.
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.
1283266
A guided clothoid spline
Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.
10283778
An Internet-based platform for testing generation scheduling auctions
The paper describes the uses and architecture of a network-centered computing-rich software platform called PowerWeb. PowerWeb was designed and built as a simulation environment for experimentally testing various power exchange auction markets through tournaments. It is designed to host simulations of a competitive "day-ahead" electric energy market in the content of a restructured electric power industry. The PowerWeb environment is meant to be flexible so as to accommodate different "rules of the game". The authors describe its interactive, distributed and Web-based character.
16046081
A method for classifying offer strategies observed in an electricity market
The idea that large-scale generating units will operate at marginal cost when given the ability to offer their power for sale in a uniform price auction is at best wishful thinking. In fact, both real and experimental data show that the more uncertainty a supplier faces (e.g., load uncertainty, uncertainty of other suppliers, etc.), the more they will hedge their profits through higher than marginal cost offers and through withholding units if permitted. This makes predicting unit commitment and dispatch ahead of time difficult. This paper explores characteristics of software agents that were designed based on the outcome of human subject experiments on a uniform price auction with stochastic load. The agent behavior is compared to the behavior of the subjects. Both subject and agent behavior is classified based on the data. Differences and similarities are noted and explained. Based on the result of the simulation, a model was suggested to explain an offer submitted in deregulated markets based on double layer diffusion.