Related papers: The simultaneous conjugacy problem in the symmetri…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
We give refined estimates for the discrete time and continuous time versions of some basic random walks on the symmetric and alternating groups $S_n$ and $A_n$. We consider the following models: random transposition, transpose top with…
The problem of determining which permutations can be sorted using certain switchyard networks dates back to Knuth in 1968. In this work, we are interested in permutations which are sortable on a double-ended queue (called a deque), or on…
We study the existence of subharmonic solutions in the system $\ddot {u}(t)=f(t,u(t))$, where $u(t)\in\mathbb{R}^{k}$ and $f$ is an even and $p$-periodic function in time. Under some additional symmetry conditions on the function $f$, the…
We give an algorithm for the hidden subgroup problem for the dihedral group $D_N$, or equivalently the cyclic hidden shift problem, that supersedes our first algorithm and is suggested by Regev's algorithm. It runs in $\exp(O(\sqrt{\log…
Subset-Sum is an NP-complete problem where one must decide if a multiset of $n$ integers contains a subset whose elements sum to a target value $m$. The best-known classical and quantum algorithms run in time $\tilde{O}(2^{n/2})$ and…
We develop and analyze concurrent algorithms for the disjoint set union (union-find) problem in the shared memory, asynchronous multiprocessor model of computation, with CAS (compare and swap) or DCAS (double compare and swap) as the…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to…
In this note, following suggestions by Tao, we extend the randomized algorithm for linear equations over prime fields by Raghavendra to a randomized algorithm for linear equations over the reals. We also show that the algorithm can be…
We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices $V$ and a permutation group $\Gamma$ over domain $V$, and asking whether there is a permutation $\gamma \in \Gamma$ that…
Kallampally and Tewari showed in 2016 that there can be a trade-off between determinism and time in space-bounded computations. This they did by describing an unambiguous non-deterministic algorithm to solve Directed Graph Reachability that…
We consider the selection problem on a completely connected network of $n$ processors with no shared memory. Each processor initially holds a given numeric item of $b$ bits allowed to send a message of $\max ( b, \lg n )$ bits to another…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
Undirected $st$-connectivity is important both for its applications in network problems, and for its theoretical connections with logspace complexity. Classically, a long line of work led to a time-space tradeoff of $T=\tilde{O}(n^2/S)$ for…
The left-invariant sub-Riemannian problem on the Engel group is considered. This problem is very important as nilpotent approximation of nonholonomic systems in four-dimensional space with two-dimensional control, for instance of a system…
Given a signed permutation on $n$ elements, we need to sort it with the fewest reversals. This is a fundamental algorithmic problem motivated by applications in comparative genomics, as it allows to accurately model rearrangements in small…
We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works…
We study the self-stabilizing leader election (SS-LE) problem in the population protocol model, assuming exact knowledge of the population size $n$. Burman, Chen, Chen, Doty, Nowak, Severson, and Xu [BCC+21] (PODC) showed that this problem…