Distinguishing between SUSY and Littlest Higgs Model using trileptons at the LHC

Littlest Higgs model with T-parity and Minimal Supersymmtric standard Model with R-parity both give similar signatures in collider experiment with a huge amount of missing energy depending upon mass of the lightest T-odd/R-odd particle. In this talk, I will discuss possibility of distinguishing the two models at the LHC in hadronically quiet signal where masses of R-odd particles are identical to masses of T-odd particles.Comment: To appear in the proceedings of Supersymmetry and the Unification of Fundamental Interactions (SUSY'09), Boston, US

Online Steiner Tree with Deletions

In the online Steiner tree problem, the input is a set of vertices that appear one-by-one, and we have to maintain a Steiner tree on the current set of vertices. The cost of the tree is the total length of edges in the tree, and we want this cost to be close to the cost of the optimal Steiner tree at all points in time. If we are allowed to only add edges, a tight bound of $\Theta(\log n)$ on the competitiveness is known. Recently it was shown that if we can add one new edge and make one edge swap upon every vertex arrival, we can maintain a constant-competitive tree online. But what if the set of vertices sees both additions and deletions? Again, we would like to obtain a low-cost Steiner tree with as few edge changes as possible. The original paper of Imase and Waxman had also considered this model, and it gave a greedy algorithm that maintained a constant-competitive tree online, and made at most $O(n^{3/2})$ edge changes for the first $n$ requests. In this paper give the following two results. Our first result is an online algorithm that maintains a Steiner tree only under deletions: we start off with a set of vertices, and at each time one of the vertices is removed from this set: our Steiner tree no longer has to span this vertex. We give an algorithm that changes only a constant number of edges upon each request, and maintains a constant-competitive tree at all times. Our algorithm uses the primal-dual framework and a global charging argument to carefully make these constant number of changes. We then study the natural greedy algorithm proposed by Imase and Waxman that maintains a constant-competitive Steiner tree in the fully-dynamic model (where each request either adds or deletes a vertex). Our second result shows that this algorithm makes only a constant number of changes per request in an amortized sense.Comment: An extended abstract appears in the SODA 2014 conferenc