Algebraic languages are at the heart of many successful optimization modeling systems, yet they have been used with only limited success for combinatorial (or discrete) optimization. We show in this paper, through a series of examples, how an algebraic modeling language might be extended to help with a greater variety of combinatorial optimization problems. We consider specifically those proble...

We work with a smooth relative curve $X_U/U$ nodal reduction over an excellent and locally factorial scheme $S$. show that blowing up model of $X_U$ in the ideal sheaf section yields new model, describe how these models relate to each other. construct N\'eron for Jacobian $X_U$, it on $S$ as quotient Picard space well-chosen model. provide combinatorial criterion be separated.

A static load-balancing scheme is discussed for numerical simulation system NSL, which automatically generates parallel solver of partial differential equations, PDE, from high level description of problem. NSL partitions computational domain into multiple blocks, and allocates processors optimally for each block in accordance with computation and communication cost. This allocation problem is ...

We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making each decision, the learner observes the losses associated with its action, but not other losses. The performance of the learner is measured in te...

Combinatorial Mobile IP, a new mobility management scheme for Mobile IP, is proposed and analyzed. We present how to adopt mobility management schemes on cellular networks and adapt them in Mobile IP without disrupting the nature of the Internet. We apply widely used mobility management schemes such as hierarchical architecture and paging in cellular networks to Mobile IP. We restrict paging to...

We consider the problem of sampling from a probability distribution defined over a high-dimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higher-dimensional space which is then randomly projected using universal hash functions to a lower-dimensional subspace and explored using combinatorial sear...

With this article I want to take the opportunity to sketch the development of topological proofs in discrete mathematics beginning with the proof of the Kneser conjecture about 25 years ago, which eventually led to a new discipline: topological combinatorics. In the beginning of the twentieth century the discipline of combinatorial topology already made use of combinatorial concepts in topology...

In a traditional (H,r) combination network, each user connects to unique set of r relays. However, few research efforts have considered the (H,r,u) multiaccess network problem wherein relays is connected by u users. this paper, we focus on designing coded caching schemes for network. By directly applying well-known coding method (proposed Zewail and Yener) scheme (called ZY scheme) obtained. it...

Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bound...

We present an annotation scheme and combinatorial authoring procedure by which a small base of annotated human-authored dialogue exchanges can be exploited to automatically generate many new exchanges. The combinatorial procedure builds recombinant exchanges by reasoning about individual lines of dialogue in terms of their mark-up, which is attributed during annotation and captures what a line ...