We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (i.e., scoring matrices). In the simple version, in which only the pattern or only the text is uncertain, we obtain efficient algorithms with theoretically-provable running times using a...

In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called k-length interval graphs were considered in which the number of different lengths of intervals is limited by k. Even after decades of research, no insight into their structure is known and the complexity of recognition is open...

Given an edge-weighted undirected graph G = (V, E, w), the density of S subseteq V is defined as w(S)/|S|, where w(S) is the sum of weights of the edges in the subgraph induced by S. The densest subgraph problem asks for S subseteq V that maximizes the density w(S)/|S|. The problem has received significant attention recently because it can be solved exactly in polynomial time...

The modularity is a quality function in community detection, which was introduced by Newman and Girvan [Phys. Rev. E, 2004]. Community detection in graphs is now often conducted through modularity maximization: given an undirected graph G = (V, E), we are asked to find a partition C of V that maximizes the modularity. Although numerous algorithms have been developed to date, most...

In this paper, we introduce maximum composition ordering problems. The input is n real functions f_1 , ... , f_n : R to R and a constant c in R. We consider two settings: total and partial compositions. The maximum total composition ordering problem is to compute a permutation sigma : [n] to [n] which maximizes f_{sigma(n)} circ f_{sigma(n-1)} circ ... circ f_{sigma(1)}(c), where...

In this paper, we study the effect of surrogate objective functions in optimization problems. We introduce surrogate ratio as a measure of such effect, where the surrogate ratio is the ratio between the optimal values of the original and surrogate objective functions. We prove that the surrogate ratio is at most mu^{|1/p - 1/q|} when the objective functions are p- and q-norms...

We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = (V, E) with a maximum edge size f. Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the...

We revisit the waiting time of patterns in repeated independent experiments. We show that the most intuitive approach for computing the waiting time, which reduces it to computing the stopping time of a Markov chain, is optimum from the perspective of computational complexity. For the single pattern case, this approach requires us to solve a system of m linear equations, where m...

We address the following question in the average-case complexity: does there exists a language L such that for all easy distributions D the distributional problem (L, D) is easy on the average while there exists some more hard distribution D' such that (L, D') is hard on the average? We consider two complexity measures of distributions: the complexity of sampling and the...

Given two independent sets I and J of a graph G, imagine that a token (coin) is placed on each vertex in I. Then, the Sliding Token problem asks if one could transforms I to J using a sequence of elementary steps, where each step requires sliding a token from one vertex to one of its neighbors, such that the resulting set of vertices where tokens are placed still remains...

In this paper, we investigate "gap problems", which are promise problems where YES instances are flexibly satisfiable in a certain sense, and NO instances are not satisfiable at all. These gap problems generalise a family of constraint-related decision problems, including the constraint satisfaction problem itself, the separation problem (can distinct variables be validly...

We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not assigning an item to any of the bins is not free in general and can potentially be the most expensive option. The goal is to minimize the...

Given a string X[1, n] and a position k in [1, n], the Shortest Unique Substring of X covering k, denoted by S_k, is a substring X[i, j] of X which satisfies the following conditions: (i) i leq k leq j, (ii) i is the only position where there is an occurrence of X[i, j], and (iii) j - i is minimized. The best-known algorithm [Hon et al., ISAAC 2015] can find S k for all k in [1...

In a standard f-connectivity network design problem, we are given an undirected graph G = (V, E), a cut-requirement function f : 2^V to N, and non-negative costs c(e) for all e in E. We are then asked to find a minimum-cost vector x in N^E such that x(delta(S)) geq f (S) for all S subseteq V. We focus on the class of such problems where f is a proper function. This encodes many...

We provide a spectrum of results for the Universal Guard Problem, in which one is to obtain a small set of points ("guards") that are "universal" in their ability to guard any of a set of possible polygonal domains in the plane. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of n vertices, or to...

The maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several...

We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of n items and that the available workspace is Theta(s) bits, where lg n <= s <= n * lg n. Three techniques that can be used as general tools in different space-efficient algorithms are introduced and employed within our algorithms. In...

Given a permutation of n elements, stored as an array, we address the problem of replacing the permutation by its kth power. We aim to perform this operation quickly using o(n) bits of extra storage. To this end, we first present an algorithm for inverting permutations that uses O(lg^2 n) additional bits and runs in O(n lg n) worst case time. This result is then generalized to...

Consider a complete weighted bipartite graph G in which each left vertex u has two real numbers intercept and slope, each right vertex v has a real number quality, and the weight of any edge (u, v) is defined as the intercept of u plus the slope of u times the quality of v. Let m (resp., n) denote the number of left (resp., right) vertices, and assume that m geq n. We develop a...

We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes C, we have P^C belongs to PostBPP or PostBQP? While a complete answer to the above question seems impossible given the development of present computational...

Let G = (V, E) be a graph modelling a building or road network in which edges have-both travel times (lengths) and capacities associated with them. An edge�s capacity is the number of people that can enter that edge in a unit of time. In emergencies, people evacuate towards the exits. If too many people try to evacuate through the same edge, congestion builds up and slows down...

We study the max-min fair allocation problem in which a set of m indivisible items are to be distributed among n agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item j on agent i is either 0 or some non-negative weight w_j. For this setting, Asadpour et al. [TALG, 2012] showed that a certain configuration-LP can...

Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014) reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of depth first search (DFS) of a graph on n vertices and m edges, taking O(m lg lg n) time using O(n) bits of space improving on the time bound of O(m lg n) due...

We study the online bounded-delay packet scheduling problem (PacketScheduling), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well...

The problem Max W-Light (Max W-Heavy) for an undirected graph is to assign a direction to each edge so that the number of vertices of outdegree at most W (resp. at least W) is maximized. It is known that these problems are NP-hard even for fixed W. For example, Max 0-Light is equivalent to the problem of finding a maximum independent set. In this paper, we show that for any fixed...