Related papers: The consensus number of a shift register equals it…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
We revisit the mergeable dictionaries with shift problem, where the goal is to maintain a family of sets subject to search, split, merge, make-set, and shift operations. The search, split, and make-set operations are the usual well-known…
The paper proposes an alternative proof that Omega, an oracle that outputs a process identifier and guarantees that eventually the same correct process identifier is output at all correct processes, provides minimal information about…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
The well-known middle levels conjecture asserts that for every integer $n\geq 1$, all binary strings of length $2(n+1)$ with exactly $n+1$ many 0s and 1s can be ordered cyclically so that any two consecutive strings differ in swapping the…
Logarithmic number systems (LNS) are used to represent real numbers in many applications using a constant base raised to a fixed-point exponent making its distribution exponential. This greatly simplifies hardware multiply, divide and…
The so-called "width law" for Liesegang patterns, which states that the positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha} for some \alpha>0, is investigated both experimentally and theoretically. We provide…
Is there an equilibrium for distributed consensus when all agents except one collude to steer the decision value towards their preference? If an equilibrium exists, then an $n-1$ size coalition cannot do better by deviating from the…
In this work, we introduce the notion of decisional width of a finite relational structure and the notion of decisional width of a regular class of finite structures. Our main result states that given a first-order formula {\psi} over a…
The protocols of distributed consensus normally aim to tolerate different types of faults including crash faults and byzantine faults that occur in the distributed systems. However, the dynamic network topology and stochastic wireless…
Consensus algorithms play a critical role in blockchains and directly impact their performance. During consensus processing, nodes need to validate and order the pending transactions into a new block, which requires verifying the…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
The consensus problem is a fundamental problem in distributed systems. It involves a set of actors, or entities, that need to agree on some values or decisions. The Raft algorithm is a solution to the consensus problem that has gained…
We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices. We treat the case of Wishart matrices $W = XX^*$ where $X$…
We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any…
Let x, y be strings of equal length. The Hamming distance h(x,y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x,y), the Hamming distance…
We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with no-consensus and the state with complete consensus in…
We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…
An online truthful budgeted matching problem is considered for a bipartite graph, where the right vertices are available ahead of time, and individual left vertices arrive sequentially. On arrival of a left vertex, its edge utilities (or…
The egalitarian processor sharing model is viewed as a restless bandit and its Whittle indexability is established. A numerical scheme for computing the Whittle indices is provided, along with supporting numerical experiments.