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A knot in a directed graph $G$ is a strongly connected subgraph $Q$ of $G$ with at least two vertices, such that no vertex in $V(Q)$ is an in-neighbor of a vertex in $V(G)\setminus V(Q)$. Knots are important graph structures, because they characterize the existence of deadlocks in a classical distributed computation m... |
We give a new algorithm for performing the distinct-degree factorization of a polynomial P(x) over GF(2), using a multi-level blocking strategy. The coarsest level of blocking replaces GCD computations by multiplications, as suggested by Pollard (1975), von zur Gathen and Shoup (1992), and others. |
(see paper for full abstract) <br>We show that the Edge-Disjoint Paths problem is W[1]-hard parameterized by the number $k$ of terminal pairs, even when the input graph is a planar directed acyclic graph (DAG). This answers a question of Slivkins (ESA '03, SIDMA '10). |
We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of $m$ indivisible goods to $n$ players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known to have an integrality gap of $\frac{3}{4}$, which matches the best known appr... |
We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. |
We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of ... |
Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for obtaining such a coloring, even for constant degree graphs. |
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place, that is to use as little auxiliary memory as possible. |
The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament maintaining given constraints. Most of the instances of this problem with more than te... |
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle interactions, and machine learning. For these problems, which can be represent... |
Gale and Shapley's stable assignment problem has been extensively studied, applied, and extended. In the context of school choice, mechanisms often aim at finding an assignment that is more favorable to students. |
The number of IoT devices is expected to continue its dramatic growth in the coming years and, with it, a growth in the amount of data to be transmitted, processed and stored. Compression techniques that support analytics directly on the compressed data could pave the way for systems to scale efficiently to these grow... |
A target set selection model is a graph $G$ with a threshold function $\tau:V\to \mathbb{N}$ upper-bounded by the vertex degree. For a given model, a set $S_0\subseteq V(G)$ is a target set if $V(G)$ can be partitioned into non-empty subsets $S_0,S_1,\dotsc,S_t$ such that, for $i \in \{1, \ldots, t\}$, $S_i$ contains ... |
We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the {\em Rectilinear Steiner Arborescence} ($RSA$). |
Best-Fit is one of the most prominent and practically used algorithms for the bin packing problem, where a set of items with associated sizes needs to be packed in the minimum number of unit-capacity bins. Kenyon [SODA '96] studied online bin packing under random-order arrival, where the adversary chooses the list... |
In this work we study shortest path problems in multimode graphs, a generalization of the min-distance measure introduced by Abboud, Vassilevska W. and Wang in [SODA'16]. A multimode shortest path is the shortest path using one of multiple `modes' of transportation that cannot be combined. |
Many data dissemination and publish-subscribe systems that guarantee the privacy and authenticity of the participants rely on symmetric key cryptography. An important problem in such a system is to maintain the shared group key as the group membership changes. |
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster approximation algorithms that avoid these relaxations, for two well-studied special case... |
Generalised hypertree width ($ghw$) is a hypergraph parameter that is central to the tractability of many prominent problems with natural hypergraph structure. Computing $ghw$ of a hypergraph is notoriously hard. |
We propose a method to exponentially speed up computation of various fingerprints, such as the ones used to compute similarity and rarity in massive data sets. Rather then maintaining the full stream of $b$ items of a universe $[u]$, such methods only maintain a concise fingerprint of the stream, and perform computati... |
The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed ... |
In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such that each elastic-degenerate symbol corresponds to a set of two or more vari... |
Carpooling, or sharing a ride with other passengers, holds immense potential for urban transportation. Ridesharing platforms enable such sharing of rides using real-time data. |
The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in $k$ colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any $k\ge 2$, there is no algorithm for Rainbow k-Coloring running in time ... |
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. |
We consider the problem of efficiently solving a system of $n$ non-linear equations in ${\mathbb R}^d$. Addressing Smale's 17th problem stated in 1998, we consider a setting whereby the $n$ equations are random homogeneous polynomials of arbitrary degrees. |
Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time for polynomially sized alphabets. |
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs. Efficient counting algorithms typically apply to ``high-temperature'' proble... |
Given a planar graph G and a sequence C_1,...,C_q, where each C_i is a family of vertex subsets of G, we wish to find a plane embedding of G, if any exists, such that for each i in {1,...,q}, there is a face F_i in the embedding whose boundary contains at least one vertex from each set in C_i. This problem has applica... |
We study the online budgeted allocation (also called ADWORDS) problem, where a set of impressions arriving online are allocated to a set of budget-constrained advertisers to maximize revenue. Motivated by connections to Internet advertising, several variants of this problem have been studied since the seminal work of ... |
The question of the definition of what is an algorithm is recurrent. It is found in teaching, at different levels and particularly in secondary education because of the recent evolutions in high school, with immediate consequences in higher education. |
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological surveys and contagious disease surveillance. |
Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. |
We show sublinear-time algorithms for Max Cut and Max E2Lin$(q)$ on expanders in the adjacency list model that distinguishes instances with the optimal value more than $1-\varepsilon$ from those with the optimal value less than $1-\rho$ for $\rho \gg \varepsilon$. The time complexities for Max Cut and Max $2$Lin$(q)$ ... |
We obtain approximation ratio $2(2+\frac{1}{\ell})$ for the (undirected) $k$-Connected Subgraph problem, where $\ell \approx \frac{1}{2} (\log_k n-1)$ is the largest integer such that $2^{\ell-1} k^{2\ell+1} \leq n$. For large values of $n$ this improves the $6$-approximation of Cheriyan and Végh when $n =\Omega(k^3)$... |
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. |
A degenerate or indeterminate string on an alphabet $\Sigma$ is a sequence of non-empty subsets of $\Sigma$. Given a degenerate string $t$ of length $n$, we present a new method based on the Burrows--Wheeler transform for searching for a degenerate pattern of length $m$ in $t$ running in $O(mn)$ time on a constant siz... |
It has been observed that many complex real-world networks have certain properties, such as a high clustering coefficient, a low diameter, and a power-law degree distribution. A network with a power-law degree distribution is known as scale-free network. |
This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under the Strong Exponential Time Hypothesis the quadratic running time cannot be be... |
We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word $w$ into another word, called the reduced word of $w$, that will be at least twice shorter; then, the algorithm recursively computes the suffix array of the reduc... |
The current best algorithms for convex body chasing problem in online algorithms use the notion of the Steiner point of a convex set. In particular, the algorithm which always moves to the Steiner point of the request set is $O(d)$ competitive for nested convex body chasing, and this is optimal among memoryless algori... |
In the Directed Disjoint Paths problem, we are given a digraph $D$ and a set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, and the task is to find a collection of pairwise vertex-disjoint paths $\{P_1, \ldots, P_k\}$ such that each $P_i$ is a path from $s_i$ to $t_i$ in $D$. This problem is NP-complete for fixed $... |
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such as large genomic collections of the same species. |
Graph construction, a fundamental operation in a data processing pipeline, is typically done by multiplying the incidence array representations of a graph, $\mathbf{E}_\mathrm{in}$ and $\mathbf{E}_\mathrm{out}$, to produce an adjacency array of the graph, $\mathbf{A}$, that can be processed with a variety of algorithms... |
We study the complexity of a generic hitting problem H-Subgraph Hitting, where given a fixed pattern graph $H$ and an input graph $G$, the task is to find a set $X \subseteq V(G)$ of minimum size that hits all subgraphs of $G$ isomorphic to $H$. In the colorful variant of the problem, each vertex of $G$ is precolored ... |
The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. |
Typing methods are widely used in the surveillance of infectious diseases, outbreaks investigation and studies of the natural history of an infection. And their use is becoming standard, in particular with the introduction of High Throughput Sequencing (HTS). |
With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. |
TSP is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on metric graphs but becomes NP-hard to approximate within any computable function $f(n)$ on general graphs. |
In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. |
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. |
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. |
The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is a vertex in the set which has distinct distances to x and y. |
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy that allows us to obtain linear-time constant-factor approximation algorithms for... |
In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(m\sqrt{\log n \cdot \log\log n})$ in the comparison-addition model. This is the first algorithm to break the $O(m+n\log n)$ time bound for real-weighted sparse... |
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. |
In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| \leq 1$ and there are at most $k$ edges with one endpoint in $A$ and the other in $B$. |
We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the special cases of p-groups and solvable groups --- ever since the n^(log n + O(1))... |
In recent years, binary quadratic programming (BQP) has been successively applied to solve several combinatorial optimization problems. We consider in this paper a study of using the BQP model to solve the minimum sum coloring problem (MSCP). |
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of $T$ days in which given demands for the items must be satisfied. |
A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_1,\varepsilon)$-clusterable if there are $k_1$ balls of radius $\varepsilon$ that cover $S$. A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_2,\delta)$-far from being clusterable if there are at least $k_2$ vectors in $S$, with all pairwise distances at least $\del... |
The min-diameter of a directed graph $G$ is a measure of the largest distance between nodes. It is equal to the maximum min-distance $d_{min}(u,v)$ across all pairs $u,v \in V(G)$, where $d_{min}(u,v) = \min(d(u,v), d(v,u))$. |
A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol to solve the message forwarding problem in a message-switched network. |
Given an indeterminate string pattern $p$ and an indeterminate string text $t$, the problem of order-preserving pattern matching with character uncertainties ($\mu$OPPM) is to find all substrings of $t$ that satisfy one of the possible orderings defined by $p$. When the text and pattern are determinate strings, we are... |
We present a work optimal algorithm for parallel fully batch-dynamic maximal matching against an oblivious adversary. In particular it processes batches of updates (either insertions or deletions of edges) in constant expected amortized work per edge update, and in $O(\log^3 m)$ depth per batch whp, where $m$ is the m... |
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. |
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . |
We study the question of whether a sequence d = (d_1,d_2, \ldots, d_n) of positive integers is the degree sequence of some outerplanar (a.k.a. 1-page book embeddable) graph G. If so, G is an outerplanar realization of d and d is an outerplanaric sequence. The case where \sum d \leq 2n - 2 is easy, as d has a realizati... |
Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging leads to a time-series decomposition. |
We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core model, a well-studied discrete spin system. |
Data compaction is a new approach for lossless and lossy compression of read-only array data. The biggest advantage over existing approaches is the possibility to access compressed data without any decompression. |
We present a simple algorithm for computing the document array given a string collection and its suffix array as input. Our algorithm runs in linear time using constant additional space for strings from constant alphabets. |
Samplers are the backbone of the implementations of any randomised algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. |
We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently, string graphs). We show that they both remain $\mathsf{NP}$-hard on $B_0$-VPG graphs admitting a representation such that each grid-edge belongs to at most one path and each horizontal path has length at most two. |
We present ABRA, a suite of algorithms that compute and maintain probabilistically-guaranteed, high-quality, approximations of the betweenness centrality of all nodes (or edges) on both static and fully dynamic graphs. Our algorithms rely on random sampling and their analysis leverages on Rademacher averages and pseud... |
Breadth-first Search (BFS) is one of the most important graph processing subroutines, especially for computing the unweighted distance. Many applications may require running BFS from multiple sources. |
The $k$-Detour problem is a basic path-finding problem: given a graph $G$ on $n$ vertices, with specified nodes $s$ and $t$, and a positive integer $k$, the goal is to determine if $G$ has an $st$-path of length exactly $\text{dist}(s, t) + k$, where $\text{dist}(s, t)$ is the length of a shortest path from $s$ to $t$.... |
Given a bipartite graph $G=(V_b,V_r,E)$, the $2$-Level Quasi-Planarity problem asks for the existence of a drawing of $G$ in the plane such that the vertices in $V_b$ and in $V_r$ lie along two parallel lines $\ell_b$ and $\ell_r$, respectively, each edge in $E$ is drawn in the unbounded strip of the plane delimited by... |
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to maintain a minimum-weight sub-graph that satisfies all the connectivity requirement... |
We introduce space- and time-efficient algorithms and data structures for the offline set intersection problem. We show that a sorted integer set $S \subseteq [0{. |
Data is continuously generated by modern data sources, and a recent challenge in machine learning has been to develop techniques that perform well in an incremental (streaming) setting. In this paper, we investigate the problem of private machine learning, where as common in practice, the data is not given at once, bu... |
We introduce the notion of delineation. A graph class $\mathcal C$ is said delineated if for every hereditary closure $\mathcal D$ of a subclass of $\mathcal C$, it holds that $\mathcal D$ has bounded twin-width if and only if $\mathcal D$ is monadically dependent. |
Derandomization is one of the classic topics studied in the theory of parallel computations, dating back to the early 1980s. Despite much work, all known techniques lead to deterministic algorithms that are not work-efficient. |
A factorization $f_1, \ldots, f_m$ of a string $w$ of length $n$ is called a repetition factorization of $w$ if $f_i$ is a repetition, i.e., $f_i$ is a form of $x^kx'$, where $x$ is a non-empty string, $x'$ is a (possibly-empty) proper prefix of $x$, and $k \geq 2$. Dumitran et al. |
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. |
Online algorithms are usually analyzed using the notion of competitive ratio which compares the solution obtained by the algorithm to that obtained by an online adversary for the worst possible input sequence. Often this measure turns out to be too pessimistic, and one popular approach especially for scheduling proble... |
The research of attribute characters in information system which contains core, necessary, unnecessary is a basic and important issue in attribute reduct. Many methods for the judgement of attribute characters are based on the relationship between the objects and attributes. |
Johnson-Lindenstrauss embeddings are widely used to reduce the dimension and thus the processing time of data. To reduce the total complexity, also fast algorithms for applying these embeddings are necessary. |
A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. |
In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In recent years, significant effort has been devoted to the study of metric $k$-c... |
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this formulation is applicable in these domains. |
In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erdös-Rényi graphs with connection probability given by $\lambda/n^\alpha$ (with $\lambda > 0$ and $0 < \alpha < 1$), a family of local algorithms that approximat... |
Correlation Clustering is a powerful graph partitioning model that aims to cluster items based on the notion of similarity between items. An instance of the Correlation Clustering problem consists of a graph $G$ (not necessarily complete) whose edges are labeled by a binary classifier as ``similar'' and ``diss... |
In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a rooted binary tree with $n$ leaves, each corresponding to one element. |
Numerous studies show that most known real-world complex networks share similar properties in their connectivity and degree distribution. They are called small worlds. |
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of $n^{1-\delta}$ for any $\delta>0$. |
Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicativ... |
We give an algorithm for augmenting the edge connectivity of an undirected graph by using the isolating cuts framework (Li and Panigrahi, FOCS '20). Our algorithm uses poly-logarithmic calls to any max-flow algorithm, which yields a running time of $\tilde O(m + n^{3/2})$ and improves on the previous best time of ... |
Motivated by the problem of storing coloured de Bruijn graphs, we show how, if we can already support fast select queries on one string, then we can store a little extra information and support fairly fast select queries on a similar string. |
A new model of causal failure is presented and used to solve a novel replica placement problem in data centers. The model describes dependencies among system components as a directed graph. |
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