Related papers: Communication Complexity of Collision
The principal angles between binary collision subspaces in an $N$-billiard system in $d$-dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of…
Brouwer's fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…
Expansions are provided for the moments of the number of collisions $X_n$ in the $\beta(2,b)$-coalescent restricted to the set $\{1,...,n\}$. We verify that $X_n/\mathbb{E}X_n$ converges almost surely to one and that $X_n$, properly…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
We introduce a new problem which we call the Pony Express problem. n robots with differing speeds are situated over some domain. A message is placed at some commonly known point. Robots can acquire the message either by visiting its initial…
Quantum resources can be more powerful than classical resources - a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two people's inputs can be done with exponentially…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…
For a prime p and base b, the digit function delta(r) = floor(br/p) partitions the residues {1, ..., p-1} into b contiguous bins. The collision count C(g) records how many residues share a bin with their image under multiplication by g. We…
Let us consider a collection $\mathcal G$ of codewords of length $n$ over an alphabet of size $s$. Let $t_1,\ldots, t_s$ be nonnegative integers. What is the maximum of $|\mathcal G|$ subject to the condition that any two codewords should…
Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain…
We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signal hashing problem…
By far the most fruitful technique for showing lower bounds for the CONGEST model is reductions to two-party communication complexity. This technique has yielded nearly tight results for various fundamental problems such as distance…
Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…
Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${\sim}\log n/\log\log n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29…