Related papers: Minmax-Regret $k$-Sink Location on a Dynamic Tree …
In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then…
We study the {\em $k$-route} generalizations of various cut problems, the most general of which is \emph{$k$-route multicut} ($k$-MC) problem, wherein we have $r$ source-sink pairs and the goal is to delete a minimum-cost set of edges to…
This paper addresses resource allocation problem with a separable objective function under a single linear constraint, formulated as maximizing $\sum_{j=1}^{n}R_j(x_j)$ subject to $\sum_{j=1}^{n}x_j=k$ and $x_j\in\{0,\dots,m\}$. While…
We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…
The 1-Steiner tree problem, the problem of constructing a Steiner minimum tree containing at most one Steiner point, has been solved in the Euclidean plane by Georgakopoulos and Papadimitriou using plane subdivisions called oriented…
We study the problem of collective tree exploration in which a team of $k$ mobile agents must collectively visit all nodes of an unknown tree in as few moves as possible. The agents all start from the root and discover adjacent edges as…
Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
The Backup Placement problem in networks in the $\mathcal{CONGEST}$ distributed setting considers a network graph $G = (V,E)$, in which the goal of each vertex $v \in V$ is selecting a neighbor, such that the maximum number of vertices in…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
In the stabilizing consensus problem, each agent of a networked system has an input value and is repeatedly writing an output value; it is required that eventually all the output values stabilize to the same value which, moreover, must be…
While much progress has been achieved over the last decades in neuro-inspired machine learning, there are still fundamental theoretical problems in gradient-based learning using combinations of neurons. These problems, such as saddle points…
We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators…
Assisting end users to identify desired results from a large dataset is an important problem for multi-criteria decision making. To address this problem, top-k and skyline queries have been widely adopted, but they both have inherent…
We propose and study an online version of min-max optimization based on cumulative saddle points under a variety of performance measures beyond convex-concave settings. After first observing the incompatibility of (static) Nash equilibrium…
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…
We consider the problem of finding maximum flows in planar graphs with capacities on both vertices and edges and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in $O(n…
We consider the k-disjoint-clique problem. The input is an undirected graph G in which the nodes represent data items, and edges indicate a similarity between the corresponding items. The problem is to find within the graph k disjoint…
We study the problem of dynamic regret minimization in online convex optimization, in which the objective is to minimize the difference between the cumulative loss of an algorithm and that of an arbitrary sequence of comparators. While the…