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Integer programs (IPs) are one of the fundamental tools used to solve combinatorial problems in theory and practice. Understanding the structure of solutions of IPs is thus helpful to argue about the existence of solutions with a certain simple structure, ...
In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the p-adic pushforward of the Haar measure under a ...
The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one- ...
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algo ...
In this thesis, we explore techniques for the development of recursive functional programs over unbounded domains that are proved correct according to their high-level specifications. We present algorithms for automatically synthesizing executable code, st ...
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...
Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...
Multi-party fair exchange (MFE) and fair secure multi-party computation (fair SMPC) are under-studied fields of research, with practical importance. We examine MFE scenarios where every participant has some item, and at the end of the protocol, either ever ...
We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by ...
We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by ...
