We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describ...

This paper provides an algebraic background for the formal derivation of greedy-like algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/pr...

Borodin, Nielsen and Rackoff [5] proposed a framework for abstracting the main properties of greedy-like algorithms with emphasis on scheduling problems, and Davis and Impagliazzo [6] extended it so as to make it applicable to graph optimization problems. In this paper we propose a related model which places certain reasonable restrictions on the power of the greedy-like algorithm. Our goal is ...

In this paper we develop a framework of submodular optimization algorithms in line with the mirror-descent style of algorithms for convex optimization. We use the fact that a submodular function has both a subdifferential and a superdifferential, which enables us to formulate algorithms for both submodular minimization and maximization. This reveals a unifying framework for a number of submodul...

We consider the class of Dandelion-like codes, i.e., a class of bijective codes for coding labeled trees by means of strings of node labels. In the literature it is possible to find optimal sequential algorithms for codes belonging to this class, but, for the best of our knowledge, no parallel algorithm is reported. In this paper we present the first encoding and decoding parallel algorithms fo...

We apply the superfast divide-and-conquer MBA algorithm to possibly singular n × n Toeplitz-like integer input matrices and extend it to computations in the ring of integers modulo a power of a random prime. We choose the power which barely fits the size of a computer word; this saves word operations in the subsequent lifting steps. We extend our early techniques for avoiding degeneration while...

Nowadays, dust phenomenon is one of the important challenges in warm and dry areas. Forecasting the phenomenon before its occurrence helps to take precautionary steps to prevent its consequences. Fuzzy expert systems capabilities have been taken into account to assist and cope with the uncertainty associated to complex environments such as dust forecasting problem. This paper presents novel hyb...