We introduce the problem of augmenting graphs with sublinear memory in order to speed up replies to queries. As a concrete example, we focus on the following problem: the input is an (unpartitioned) bipartite graph G = (V,E). Given a query v ∈ V , the algorithm’s goal is to output v’s color in some legal 2-coloring of G, using few probes to the graph. All replies have to be consistent with the ...

From 17.07.05 to 22.07.05, the Dagstuhl Seminar 05291 Sublinear Algorithms was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are...

We show that Farkas’ lemma for linear inequality systems, established in 1902, continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming problems which include classes of robust linear programming problems.

We study functions whose directional derivatives can be written as a difference of two extended real valued sublinear function (ds functions). The pair of convex sets obtained as the support functions of these sublinear functions is provided by a familiar equivalence relation and is considered as the bisubdifferential of the function. We study calculus rules and give application to minimization...

A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the ‘directed polymers in a ran...

We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is optimal policy of POMDP with a known environment in terms average reward over an infinite horizon. propose algorithm this problem, building on spectral method-of-moments estimations hidden models, belief error control POMDPs and upper confidence bou...

This paper presents a new method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the scalar optimization problem constructed by using these functions, enables to compute complete set of weakly efficient, efficient, and properly efficient solutions of multi-objective optim...

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a ge...