arXiv subjects

Aris Pagourtzis

Publications and source records attributed to Aris Pagourtzis.

17 recordsLinked to original sources

arXiv2026

The Complexity of Computing Class Probabilities in BID Probabilistic Databases

We study the problem of computing class probabilities in block-independent disjoint (BID) probabilistic databases. Given the probability with which each block in the database realizes each feasible tuple type, the goal is to compute the probability of a class of worlds specified by a given tuple multiplicity vector, thus grouping together worlds with the same bag (multiset) of realized tuple types. For this problem, we prove $\#\mathsf{P}$-hardness even for very restricted and structured inputs. On the other hand, we show that it admits an FPRAS, as well as $\mathsf{XP}$-time algorithms parameterized by the number of tuple types and the treewidth of an incidence graph modeling the connections between blocks and tuples. Finally, we show that augmenting the problem with certain compatibility constraints between block realizations renders it $\#\mathsf{XLP}$- and $\#\mathsf{XALP}$-hard parameterized by pathwidth and treewidth respectively, ruling out $\mathsf{FPT}$ algorithms under standard assumptions. We leave as an open question whether this also holds in the absence of compatibility constraints.

cs.DS↗

arXiv2026

Satisfactory Budget Division

A divisible budget must be allocated to several projects, and agents are asked for their opinion on how much they would give to each project. We consider that an agent is satisfied by a division of the budget if, for at least a certain predefined number $τ$ of projects, the part of the budget actually allocated to each project is at least as large as the amount the agent requested. The objective is to find a budget division that ``best satisfies'' the agents. In this context, different problems can be stated and we address the following ones. We study $(i)$ the largest proportion of agents that can be satisfied for any instance, $(ii)$ classes of instances admitting a budget division that satisfies all agents, $(iii)$ the complexity of deciding if, for a given instance, every agent can be satisfied, and finally $(iv)$ the question of finding, for a given instance, the smallest total budget to satisfy all agents. We provide answers to these complementary questions for several natural values of the parameter $τ$, capturing scenarios where we seek to satisfy for each agent all; almost all; half; or at least one of her requests.

cs.GT↗

arXiv2026

Temporal Path Covers: Dilworth Properties and Parameterized Complexity

The Minimum Temporal Path Cover (TPC) and Minimum Temporally Disjoint Path Cover (TDPC) problems were introduced by [Chakraborty, Dailly, Foucaud, Klasing, MFCS '24]. Both were shown to be NP-hard on temporal DAGs, while the latter is also NP-hard on temporal oriented trees. All tractable cases for T(D)PC established in that paper satisfy a temporal Dilworth property, namely that the size of the minimum T(D)PC is equal to the size of the maximum antichain. This raises a natural question: is T(D)PC polynomial-time solvable under the promise that the respective Dilworth property holds? In this work, we answer this question in the affirmative for both problems, proving in fact that, under the respective promise, the size of the minimum T(D)PC is exactly equal to the Lovász number of the connectivity graph. In another direction, we establish parameterized algorithms and hardness results for TPC and TDPC. Our main result is that TPC is W[1]-hard parameterized by the deletion distance to linear forest even for temporal graphs with two time-steps, answering in the negative an open question by Chakraborty et al. about whether an XP algorithm parameterized by treewidth plus number of time-steps can be improved to FPT. On the other hand, we prove that an FPT algorithm does exist if the vertex cover number is used as parameter instead of the treewidth in the above parameterization. We complement this with a proof that including the number of time-steps in the parameter is necessary to yield tractability, as, otherwise, both TPC and TDPC remain NP-hard even for constant vertex cover size. Along the way, we establish various other para-NP-hardness results involving structural parameters such as the pathwidth and the maximum degree of the underlying graph.

cs.DS↗

arXiv2026

Finite Pinwheel Scheduling: the k-Visits Problem

Pinwheel Scheduling is a fundamental scheduling problem, in which each task $i$ is associated with a positive integer $d_i$, and the objective is to schedule one task per time slot, ensuring each task perpetually appears at least once in every $d_i$ time slots. Although conjectured to be PSPACE-complete, the complexity of Pinwheel Scheduling remains open. We introduce k-Visits, a finite version of Pinwheel Scheduling, where given n deadlines, the goal is to schedule each task exactly k times. While we observe that the 1-Visit problem is trivial, we prove that 2-Visits is strongly NP-complete through a surprising reduction from Numerical 3-Dimensional Matching (N3DM). As intermediate steps in the reduction, we define NP-complete variants of N3DM which may be of independent interest. We further extend our strong NP-hardness result to a generalization of k-Visits $k\geq 2$ in which the deadline of each task may vary throughout the schedule, as well as to a similar generalization of Pinwheel Scheduling, thus making progress towards settling the complexity of Pinwheel Scheduling. Additionally, we prove that 2-Visits can be solved in linear time if all deadlines are distinct, rendering it one of the rare natural problems which exhibit the interesting dichotomy of being in P if their input is a set and NP-complete if the input is a multiset. We achieve this through a Turing reduction from 2-Visits to a variation of N3DM, which we call Position Matching. Based on this reduction, we also show an FPT algorithm for 2-Visits parameterized by a value related to how close the input deadlines are to each other, as well as a linear-time algorithm for instances with up to two distinct deadlines.

cs.DS↗

arXiv2026

Approximation Schemes for k-Subset Sum Ratio and k-way Number Partitioning Ratio

The Subset Sum Ratio problem (SSR) asks, given a multiset $A$ of positive integers, to find two disjoint subsets of $A$ such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the $k$-version of SSR, namely $k$-Subset Sum Ratio ($k$-SSR), which asks to minimize the largest-to-smallest ratio of sums of $k$ disjoint subsets of $A$. We develop an approximation scheme for $k$-SSR running in $O({n^{2k}}/{\varepsilon^{k-1}})$ time, where $n=|A|$ and $\varepsilon$ is the error parameter. To the best of our knowledge, this is the first FPTAS for $k$-SSR for fixed $k>2$. We also study the $k$-way Number Partitioning Ratio ($k$-PART) problem, which differs from $k$-SSR in that the $k$ subsets must constitute a partition of $A$; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for $k$-PART, also achieving $O({n^{2k}}/{\varepsilon^{k-1}})$ time complexity. Notably, $k$-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the $O(n^{4k^2+1}/\varepsilon^{2k^2})$ bound obtained by Nguyen and Rothe's FPTAS for Minimum Envy-Ratio with general additive valuations. Lastly, we propose a second FPTAS for $k$-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of $\widetilde{O}(n/{\varepsilon^{3k-1}})$, thus being much faster when $n\gg 1/ \varepsilon$.

cs.DS↗

arXiv2026

Beer Path Problems in Temporal Graphs

Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas stations or convenience stops, prior to reaching the final destination, has been recently introduced and extensively studied in static graphs. However, existing approaches do not account for temporal information, which is often crucial in real-world scenarios. For instance, transit services may follow fixed schedules, and shops may only be accessible during certain hours. In this work, we introduce the notion of beer paths in temporal graphs, where edges are time-dependent and certain vertices (beer vertices) are active only at specific time instances. We formally define the problems of computing earliest-arrival, latest-departure, fastest, and shortest temporal beer paths and propose efficient algorithms for these problems under both edge stream and adjacency list representations. The time complexity of each of our algorithms is aligned with that of corresponding temporal pathfinding algorithms, thus preserving efficiency. Additionally, we present preprocessing techniques that enable efficient query answering under dynamic conditions, for example new openings or closings of shops. We achieve this through appropriate precomputation of selected paths or by transforming a temporal graph into an equivalent static graph.

cs.DS↗

arXiv2024

On the power of counting the total number of computation paths of NPTMs

In this paper, we define and study variants of several complexity classes of decision problems that are defined via some criteria on the number of accepting paths of an NPTM. In these variants, we modify the acceptance criteria so that they concern the total number of computation paths instead of the number of accepting ones. This direction reflects the relationship between the counting classes #P and TotP, which are the classes of functions that count the number of accepting paths and the total number of paths of NPTMs, respectively. The former is the well-studied class of counting versions of NP problems introduced by Valiant (1979). The latter contains all self-reducible counting problems in #P whose decision version is in P, among them prominent #P-complete problems such as Non-negative Permanent, #PerfMatch, and #DNF-Sat, thus playing a significant role in the study of approximable counting problems. We show that almost all classes introduced in this work coincide with their `#accepting paths'-definable counterparts, thus providing an alternative model of computation for them. Moreover, for each of these classes, we present a novel family of complete problems, which are defined via TotP-complete problems. This way, we show that all the aforementioned classes have complete problems that are defined via counting problems whose existence version is in P, in contrast to the standard way of obtaining completeness results via counting versions of NP-complete problems. To the best of our knowledge, prior to this work, such results were known only for parity-P and C=P.

cs.CC↗

arXiv2023

On the Approximability of External-Influence-Driven Problems

Domination problems in general can capture situations in which some entities have an effect on other entities (and sometimes on themselves). The usual goal is to select a minimum number of entities that can influence a target group of entities or to influence a maximum number of target entities with a certain number of available influencers. In this work, we focus on the distinction between \textit{internal} and \textit{external} domination in the respective maximization problem. In particular, a dominator can dominate its entire neighborhood in a graph, internally dominating itself, while those of its neighbors which are not dominators themselves are externally dominated. We study the problem of maximizing the external domination that a given number of dominators can yield and we present a 0.5307-approximation algorithm for this problem. Moreover, our methods provide a framework for approximating a number of problems that can be cast in terms of external domination. In particular, we observe that an interesting interpretation of the maximum coverage problem can capture a new problem in elections, in which we want to maximize the number of \textit{externally represented} voters. We study this problem in two different settings, namely Non-Secrecy and Rational-Candidate, and provide approximability analysis for two alternative approaches; our analysis reveals, among other contributions, that an earlier resource allocation algorithm is, in fact, a 0.462-approximation algorithm for maximum external domination in directed graphs.

cs.DS↗

arXiv2022

Approximating Subset Sum Ratio via Partition Computations

We present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to $1$ as possible. Our scheme makes use of exact and approximate algorithms for the closely related Partition problem, hence any progress over those -- such as the recent improvement due to Bringmann and Nakos [SODA 2021] -- carries over to our FPTAS. Depending on the relationship between the size of the input set $n$ and the error margin $\varepsilon$, we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity $O(n^4 / \varepsilon)$. In particular, the exponent of $n$ in our proposed scheme may decrease down to $2$, depending on the Partition algorithm used. Furthermore, while the aforementioned state of the art complexity, expressed in the form $O((n + 1 / \varepsilon)^c)$, has constant $c = 5$, our results establish that $c < 5$.

cs.DS↗

arXiv2022

Faster Algorithms for $k$-Subset Sum and Variations

We present new, faster pseudopolynomial time algorithms for the $k$-Subset Sum problem, defined as follows: given a set $Z$ of $n$ positive integers and $k$ targets $t_1, \ldots, t_k$, determine whether there exist $k$ disjoint subsets $Z_1,\dots,Z_k \subseteq Z$, such that $Σ(Z_i) = t_i$, for $i = 1, \ldots, k$. Assuming $t = \max \{ t_1, \ldots, t_k \}$ is the maximum among the given targets, a standard dynamic programming approach based on Bellman's algorithm [Bell57] can solve the problem in $O(n t^k)$ time. We build upon recent advances on Subset Sum due to Koiliaris and Xu [Koil19] and Bringmann [Brin17] in order to provide faster algorithms for $k$-Subset Sum. We devise two algorithms: a deterministic one of time complexity $\tilde{O}(n^{k / (k+1)} t^k)$ and a randomised one of $\tilde{O}(n + t^k)$ complexity. Additionally, we show how these algorithms can be modified in order to incorporate cardinality constraints enforced on the solution subsets. We further demonstrate how these algorithms can be used in order to cope with variations of $k$-Subset Sum, namely Subset Sum Ratio, $k$-Subset Sum Ratio and Multiple Subset Sum.

cs.DS↗

arXiv2020

Characterizations and approximability of hard counting classes below #P

An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible counting problems with easy decision version, thus eligible to be approximable. Indeed, most problems known so far to admit an fpras fall into this class. An open question raised recently by the community of descriptive complexity is to find a logical characterization of TotP and of robust subclasses of TotP. In this work we define two subclasses of TotP, in terms of descriptive complexity, both of which are robust in the sense that they have natural complete problems, which are defined in terms of satisfiability of Boolean formulae. We then explore the relationship between the class of approximable counting problems and TotP. We prove that TotP $\nsubseteq$ FPRAS if and only if NP $\neq$ RP and FPRAS $\nsubseteq$ TotP unless RP = P. To this end we introduce two ancillary classes that can both be seen as counting versions of RP. We further show that FPRAS lies between one of these classes and a counting version of BPP. Finally, we provide a complete picture of inclusions among all the classes defined or discussed in this paper with respect to different conjectures about the NP vs. RP vs. P questions.

cs.CC↗

arXiv2020

Approximation Schemes for Subset Sum Ratio Problems

We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional meaningful requirements. Our main contribution is a generic framework that yields fully polynomial time approximation schemes (FPTAS) for problems in this family that meet certain conditions. We use our framework to design explicit FPTASs for two such problems, namely Two-Set Subset-Sum Ratio and Factor-$r$ Subset-Sum Ratio, with running time $\mathcal{O}(n^4/\varepsilon)$, which coincides with the best known running time for the original $SSR$ problem [15].

cs.DS↗

arXiv2019

Approximate #Knapsack Computations to Count Semi-Fair Allocations

In this paper, we study the problem of counting the number of different knapsack solutions with a prescribed cardinality. We present an FPTAS for this problem, based on dynamic programming. We also introduce two different types of semi-fair allocations of indivisible goods between two players. By semi-fair allocations, we mean allocations that ensure that at least one of the two players will be free of envy. We study the problem of counting such allocations and we provide FPTASs for both types, by employing our FPTAS for the prescribed cardinality knapsack problem.

cs.CC↗

arXiv2019

Parameterized Fine-Grained Reductions

During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of fine-grained reductions, which correlate the exact complexities of problems such that improvements in their running times or hardness results are carried over. We provide a parameterized viewpoint of these reductions (PFGR) in order to further analyze the structure of improvable problems and set the foundations of a unified methodology for extending algorithmic results. In this context, we define a class of problems (FPI) that admit fixed-parameter improvements on their running time. As an application of this framework we present a truly sub-quadratic fixed-parameter algorithm for the orthogonal vectors problem. Finally, we provide a circuit characterization for FPI to further solidify the notion of improvement.

cs.CC↗

arXiv2018

A Faster FPTAS for the Subset-Sums Ratio Problem

The Subset-Sums Ratio problem (SSR) is an optimization problem in which, given a set of integers, the goal is to find two subsets such that the ratio of their sums is as close to 1 as possible. In this paper we develop a new FPTAS for the SSR problem which builds on techniques proposed in [D. Nanongkai, Simple FPTAS for the subset-sums ratio problem, Inf. Proc. Lett. 113 (2013)]. One of the key improvements of our scheme is the use of a dynamic programming table in which one dimension represents the difference of the sums of the two subsets. This idea, together with a careful choice of a scaling parameter, yields an FPTAS that is several orders of magnitude faster than the best currently known scheme of [C. Bazgan, M. Santha, Z. Tuza, Efficient approximation algorithms for the Subset-Sums Equality problem, J. Comp. System Sci. 64 (2) (2002)].

cs.DS↗

arXiv2017

Joining Local Knowledge to Communicate Reliably (Extended Abstract)

A fundamental primitive in distributed computing is Reliable Message Transmission (RMT), which refers to the task of correctly sending a message from a party (or player) to another, in a network where some intermediate relays might be controlled by an adversary. We address the problem under the realistic assumption that the topological knowledge of players is restricted to a certain subgraph and specifically study the role of local information exchange in the feasibility of RMT. We employ the General Adversary model of Hirt and Maurer and the recently introduced Partial Knowledge Model which subsume all known models for the adversary and local knowledge respectively. Tight feasibility conditions, naturally involving the network topology, the adversary and the local knowledge of players, are presented.

cs.DC↗

arXiv2016

$k$-shot Broadcasting in Ad Hoc Radio Networks

We study distributed broadcasting protocols with few transmissions (`shots') in radio networks where the topology is unknown. In particular, we examine the case in which a bound $k$ is given and a node may transmit at most $k$ times during the broadcasting protocol. Initially, we focus on oblivious algorithms for $k$-shot broadcasting, that is, algorithms where each node decides whether to transmit or not with no consideration of the transmission history. Our main contributions are (a) a lower bound of $Ω(n^2/k)$ on the broadcasting time of any oblivious $k$-shot broadcasting algorithm and (b) an oblivious broadcasting protocol that achieves a matching upper bound, namely $O(n^2/k)$, for every $k \le \sqrt{n}$ and an upper bound of $O(n^{3/2})$ for every $k > \sqrt{n}$. We also study the general case of adaptive broadcasting protocols where nodes decide whether to transmit based on all the available information, namely the transmission history known by each. We prove a lower bound of $Ω\left(n^{\frac{1+k}{k}}\right)$ on the broadcasting time of any protocol by introducing the \emph{transmission tree} construction which generalizes previous approaches.

cs.DC↗