We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytope P G of a graph G. Each \wheel connguration" gives rise to two such inequalities. The simplest wheel connguration is an \odd" subdivision W of a wheel, and for these we give necessary and suucient conditions for the wheel inequality to be facet-inducing for P W. Generalizations arise by allowin...

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a ...

The last several lectures proved that polynomial-time exact recovery is possible for instances of several NP -hard problems that satisfy some type of stability condition. Lecture #7 showed that the single-link++ algorithm, which searches over a restricted set of feasible solutions, and thus can return a suboptimal solution in worst-case instances, recovers the optimal clustering in stable k-med...

A symmetry of a game is a permutation of the player set and their strategy sets that leaves the payoff functions invariant. In this paper we introduce and discuss two relatively mild symmetry properties for set-valued solution concepts (that are equivalent when the solution concepts are singlevalued) and show using examples that stable sets satisfy neither version. These examples also show that...

let x=(xi, • • ■ , xn) and /=(fi, • • • ,/„), and suppose that / is of class C1. A set, 12, of points x will be called unrestricted if, whenever a point x0 is in 12, the solution path x = x(t), where x0 = x(0), exists for — co </< oo and lies in 12. Two types of stability distinguished simply by "A" and "B" will be considered: (A) Let the value to be arbitrary but fixed. A solution x — x(t) of ...

For the past ten years, researchers have used the Stable Paths Problem (SPP) to analyze the stability properties of the Border Gateway Protocol (BGP). Analysis of SPP has revealed several combinations of topologies and routing configurations (or gadgets) where BGP cannot converge to a unique stable solution. Researchers typically analyze SPP by hand, using a trial-anderror process to (i) genera...

Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can stated about optimal if an objective function is provided. This work goes beyond the bare enumeration of and addresses computational task solution by optimality (SEO). studied in context Answer Set Programming (ASP) where (op...

Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped set, classes of k-stable alternatives and k-stable sets. The main focus of the paper is to construct ...