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.
14962541
Efficiently four-coloring planar graphs
An outline of aquadratic algorithm to 4-color planar graphs is presented, based upon anew proof of the Four Color Theorem. This algorithm improves aquartic algorithm of Appel and Haken.
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 $L(e)$.
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.
206570506
Quickly Excluding a Planar Graph
Abstract In an earlier paper, the first two authors proved that for any planar graph H , every graph with no minor isomorphic to H has bounded tree width; but the bound given there was enormous. Here we prove a much better bound. We also improve the best known bound on the tree-width of planar graphs with no minor isomorphic to a g × g grid.
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.
17884360
Experimental results for single period auctions
The objective of the paper is to present experimental results for testing the performance of different auction mechanisms related to the introduction of competitive markets for the generation of electricity. The research is based on the concept of smart markets introduced by Vernon Smith (K.A. McCabe et al., 1991) and a simulation model (PowerWeb) of a realistic bulk power system. There are unique physical aspects associated with the supply of electricity (e.g. required instantaneous matching of supply and demand, unintended congestion of parallel transmission routes and maintenance of system stability in response to disturbances). As a result, traditional theories of efficient markets and auction structures developed for other commodities may not be efficient if applied without alteration to markets for electricity. Conversely, current utility rules of operation developed for a centrally planned regime may not be appropriate in a competitive environment. The research does not address the issues of multiperiod operations (unit commitment) and multidimensional markets (ancillary services), and considers only real power in a single time period. The main objective is to test three alternative auction mechanisms when market power is a potential problem. This situation occurs when limits on transmission lines are binding to form a load pocket in which demand is met by a few (in this case two) generators.
31409070
Hermite interpolation with a pair of spirals
Abstract The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G 2 curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.
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.
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.
13961083
Experimental tests of competitive markets for electric power
Testing the performance of electricity markets using POWERWEB has already shown that relatively inexperienced players can identify and exploit market power in load pockets. When transmission constraints are not binding, however, auctions with six players have been shown to be efficient. There is evidence from operating electricity markets that prices can be driven above competitive levels when the largest supplier controls less than 20% of total installed capacity. This is accomplished by causing price spikes to occur. In experiments, uncertainty about the actual load and paying standby costs regardless of whether or not a unit is actually dispatched contribute to volatile price behavior. The objective of this paper is to investigate characteristics of a market that affect price volatility. The tests consider three different sets of rules for setting price when there are capacity shortfalls, and the following four market structures: load is responsive to price; price forecasts are made before market settlement; a day-ahead market and a balancing market auction; and suppliers are paid actual offers (a discriminatory auction).