Related papers: Probabilistic verification algorithm for linear co…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
In this paper, a random primality proving algorithm is proposed, which generates prime certificate of length O(log n). The certificate can be verified in deterministic time O(log^4 n). The algorithm runs in heuristical time tilde{O}(log^4…
The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
We address complexity issues for linear differential equations in characteristic $p>0$: resolution and computation of the $p$-curvature. For these tasks, our main focus is on algorithms whose complexity behaves well with respect to $p$. We…
We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.
We give a polynomial-time algorithm for detecting very long cycles in dense regular graphs. Specifically, we show that, given $\alpha \in (0,1)$, there exists a $c=c(\alpha)$ such that the following holds: there is a polynomial-time…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
We consider the fundamental derandomization problem of deterministically finding a satisfying assignment to a CNF formula that has many satisfying assignments. We give a deterministic algorithm which, given an $n$-variable…
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…
We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ…
We present an $O(n^2)$-time algorithm to test whether an $n$-vertex directed partial $2$-tree is upward planar. This result improves upon the previously best known algorithm, which runs in $O(n^4)$ time.
A probabilistic version of the Weisfeiler-Leman algorithm for computing the coherent closure of a colored graph is suggested. The algorithm is Monte Carlo and runs in time $ O(n^{1+\omega}\log^2 n) $, where $ n $ is the number of vertices…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…