Related papers: On the number of $k$-cycles in the assignment prob…
Presented with a new machine with a specific interconnect topology, algorithm designers use intuition about the symmetry of the algorithm to design time and communication-efficient schedules that map the algorithm to the machine. Is there a…
The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
We study random unitary channels which reproduce the action of the twirling channel corresponding to the representation of the symmetric groupon an n-fold tensor product. We derive upper andlower bounds on the randomness cost of…
In this paper we consider two metric covering/clustering problems - \textit{Minimum Cost Covering Problem} (MCC) and $k$-clustering. In the MCC problem, we are given two point sets $X$ (clients) and $Y$ (servers), and a metric on $X \cup…
We compute the limiting distribution, as n approaches infinity, of the number of cycles of length between gamma n and delta n in a permutation of [n] chosen uniformly at random, for constants gamma, delta such that 1/(k+1) <= gamma < delta…
In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \sum_j w_j C_j$ using the three-field notation. For this problem, a…
The enumeration of Hamiltonian cycles on 2n*2n grids of nodes is a longstanding problem in combinatorics. Previous work has concentrated on counting all cycles. The current work enumerates nonisomorphic cycles -- that is, the number of…
We consider optimal swarm control problems where two different classes of agents are present. Continuum idealizations of large-scale swarms are used where the dynamics describe the evolution of the spatially-distributed densities of each…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
This paper addresses the task allocation problem for multi-robot systems. The main issue with the task allocation problem is inherent complexity that makes finding an optimal solution within a reasonable time almost impossible. To hand the…
Unlimited asynchronism is intolerable in real physically distributed computer systems. Such systems, synchronous or not, use clocks and timeouts. Therefore the magnitudes of elapsed absolute time in the system need to satisfy the axiom of…
We call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…
In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…
We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial…
Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions…
We consider discrete allocation problem where $m$ indivisible goods are to be divided among $n$ agents. When agents' valuations are additive, the well-known cycle cancelling lemma by Lenstra, Shmoys, and Tardos plays a key role in design…
Within the formalism of matrix product ansatz, we study a two-species asymmetric exclusion process with backward and forward site-ordered sequential update. This model, which was originally introduced with the random sequential update,…