Related papers: A Fast Algorithm for Online k-servers Problem on T…
We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…
Path partition problems on trees have found various applications. In this paper, we present an $O(n \log n)$ time algorithm for solving the following variant of path partition problem: given a rooted tree of $n$ nodes $1, \ldots, n$, where…
The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…
Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
The Work Function Algorithm is the most effective deterministic on-line algorithm for the k-server problem. Koutsoupias and Papadimitriou proved WFA is (2k-1) competitive. However the best known implementation of WFA requires time O(i^2) to…
The k-SERVER problem is one of the most prominent problems in online algorithms with several variants and extensions. However, simplifying assumptions like instantaneous server movements and zero service time has hitherto limited its…
In the online Steiner forest problem we are given a graph $G$, and a sequence of terminal pairs $(u_i,v_i)$ which arrive in an online fashion. We are asked to maintain a low-cost subgraph in which each $u_i$ is connected to $v_i$ for all…
We study a fundamental online scheduling problem where jobs with processing times, weights, and deadlines arrive online over time at their release dates. The task is to preemptively schedule these jobs on a single or multiple (possibly…
In the setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two…
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
We present three algorithms to compute the complexity $\Vert n\Vert$ of all natural numbers $ n\le N$. The first of them is a brute force algorithm, computing all these complexities in time $O(N^2)$ and space $O(N\log^2 N)$. The main…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…
In the k-Path problem, the input is a directed graph $G$ and an integer $k\geq 1$, and the goal is to decide whether there is a simple directed path in $G$ with exactly $k$ vertices. We give a deterministic algorithm for k-Path with time…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where $k$ vehicles of…
In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way…