Abstract We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For with singleton strategies player-specific affine cost functions, we devise first polynomial time algorithm computing a pure Nash equilibrium. Our is combinatorial computes exact assuming rational input. The idea to compute...

In this article we study the relation between flat solvmanifolds and $$G_2$$ -geometry. First, give a classification of 7-dimensional splittable using finite subgroups $$\mathsf{GL}(n,\mathbb {Z})$$ for $$n=5$$ $$n=6$$ . Then, look closed, coclosed divergence-free -structures compatible with metric on them. particular, provide explicit examples compact manifolds torsion-free -structure whose ho...

We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a 6 5 -approximation algorithm for a sp...

The power and usefulness of cleavability (also known as splittability) have been well established within the framework of topology by A.V. Arhangel’skii and his associates. The concept was transferred to partially ordered sets by D.J. Marron and T.B.M. McMaster. The connections between topology and order are here exploited as we examine the properties enjoyed by a topological space that is spli...

Let G = (V, E) be a graph with a source node s and a sink node t, |V | = n, |E| = m. For a given number k, the Maximum k–Splittable Flow Problem (MkSF) is to find an s, t–flow of maximum value with a flow decomposition using at most k paths. In the multicommodity case this problem generalizes disjoint paths problems and unsplittable flow problems. We provide a comprehensive overview of the comp...

In 2014, Steele, Lea, and Flood presented SplitMix, an object-oriented pseudorandom number generator (prng) that is quite fast (9 64-bit arithmetic/logical operations per 64 bits generated) also splittable . A conventional prng object provides a generate method returns one value updates the state of prng; has second operation, split , replaces original with two (seemingly) independent objects, ...

We say that a permutation π is merged from permutations ρ and τ , if we can color the elements of π red and blue so that the red elements are order-isomorphic to ρ and the blue ones to τ . A permutation class is a set of permutations closed under taking subpermutations. A permutation class C is splittable if it has two proper subclasses A and B such that every element of C can be obtained by me...

This paper continues the study of the the allocation of memory to processors in a pipeline problem. This problem can be modeled as a variation of bin packing where each item corresponds to a different type and the normalized weight of each item can be greater than 1, which is the size of a bin. Furthermore, in this problem, items may be split arbitrarily, but each bin may contain at most k type...

A picturesque way to see a large network of links shared by many infinitesimally small selfish users is as a large pipeline infrastructure with users as liquid molecules flowing into it. When the owner of such a selfishly congested network tries to improve its flow speed, the common sense suggests to focus and fix links that seem older and slower. Contrary to this belief, Braess's paradox illus...