Related papers: I/O-Efficient Data Structures for Colored Range an…
Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI,…
In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…
The min-rank of a digraph was shown by Bar-Yossef et al. (2006) to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this work, the graphs…
Given a set of unit-disks in the plane with union area $A$, what fraction of $A$ can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved $1/4.41$. Motivated by the problem of channel-assignment…
In this paper we study the adaptive prefix coding problem in cases where the size of the input alphabet is large. We present an online prefix coding algorithm that uses $O(\sigma^{1 / \lambda + \epsilon}) $ bits of space for any constants…
The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…
The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the…
Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…
In this paper, we present a deterministic variant of Chan's randomized partition tree [Discret. Comput. Geom., 2012]. This result leads to numerous applications. In particular, for $d$-dimensional simplex range counting (for any constant $d…
We give deterministic distributed $(1+\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\frac{1}{\epsilon} \log n)$ rounds,…
We show that for any set of $n$ points moving along "simple" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the…
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…
In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…
In this paper, we consider the problem of efficiently representing a set $S$ of $n$ items out of a universe $U=\{0,...,u-1\}$ while supporting a number of operations on it. Let $G=g_1...g_n$ be the gap stream associated with $S$, $gap$ its…
Bille and G{\o}rtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and…
In this paper we are interested in indexing texts for substring matching queries with one edit error. That is, given a text $T$ of $n$ characters over an alphabet of size $\sigma$, we are asked to build a data structure that answers the…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
In this paper, we present improved algorithms for the $(\Delta+1)$ (vertex) coloring problem in the Congested-Clique model of distributed computing. In this model, the input is a graph on $n$ nodes, initially each node knows only its…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…