Probe interval graphs are used as a generalization of interval graphs in physical mapping of DNA. is a probe interval graph (PIG) with respect to a partition of if vertices of correspond to intervals on a real line and two vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is in ; vertices belonging to are called probes and vertices belonging t...

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm’s configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using model predictive control which...

The worst-case fastest known algorithm for the Set Cover problem on universes with n elements still essentially is the simple O∗(2n)-time dynamic programming algorithm, and no non-trivial consequences of an O∗(1.01n)-time algorithm are known. Motivated by this chasm, we study the following natural question: Which instances of Set Cover can we solve faster than the simple dynamic programming alg...

This paper presents an effective approach (EXTRACOL) to coloring large graphs. The proposed approach uses a preprocessing method to extract large independent sets from the graph and a memetic algorithm to color the residual graph. Each preprocessing application identifies, with a dedicated tabu search algorithm, a number of pairwise disjoint independent sets of a given size in order to maximize...

The question of how complicated a critical set must be to have a nonnull image is answered by relating its Hausdorff dimension to the (Holder) differentiability of the map. This leads to a new extension of the Morse-Sard Theorem. The main tool is an extended version of Morse's Lemma.

----------------------------------------------------------We study the Mas-Collel bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium al...

In interactive document retrieval, we need to find relevant documents to our interest from a large data set of documents, within a few iterations of judgement on retrieved documents. In each iteration, a comparatively small batch of documents is evaluated to establish their relevance to user’s interest. This method is also called relevance feedback, and it requires both of relevant and non-rele...

Clustering has been an active research area of great practical importance for recent years. Most previous clustering models have focused on grouping objects with similar values on a (sub)set of dimensions (e.g., subspace cluster) and assumed that every object has an associated value on every dimension (e.g., bicluster). These existing cluster models may not always be adequate in capturing coher...

This article considers inverse problems of shape recovery from noisy boundary data, where the forward problem involves the inversion of elliptic PDEs. The piecewise constant solution, a scaling and translation of a characteristic function, is described in terms of a smoother level set function. A fast and simple dynamic regularization method has been recently proposed that has a robust stopping...